Going against the grain
Saying to their faces "I am not going to work during my vacation" will make me appear too full of myself, as this is not the norm in this workplace.
If you go against the norm, no matter the topic, you're going to rub people the wrong way when those people expect you to adhere to the norm. Whether that's about after hours availability, dress code, general attitude, ... doesn't matter. You're doing things differently than people expect/want you to do them.
Just to be clear, I am 100% on board with your opinion on the separation of work and private life. But you're trying to deal with people who disagree. So I'm skipping on labelling either opinion as objectively wrong or right, since this is a matter of how to deal with differing opinions.
If "the norm" at work was the belief that anyone who doesn't wear orange socks must be intent on murdering the company CEO, and you think that's a silly belief; would you still wear the orange socks?
You're not required to wear them. You may even want to not wear them as a point of principle. But it's inevitable that when you don't wear the orange socks, people will be looking at you as if you're going to kill the CEO. And if it's inevitable, you shouldn't be surprised that it happens when you don't wear the socks.
What you're asking for is how to convince everyone that what they consider to be the norm should not be applied to you. By definition of what a "norm" is, that's going to be an uphill battle, one you're much more likely to lose than win.
You're asking people to change their belief on a certain topic, based on the fact that you believe something different. When you look at it in this light, it becomes clear just how difficult this is going to be.
- I want to hold my ground regarding my vacation.
- How can I decline to solve problems for my peers, some of which I consider friends, and vice versa, without appearing something I don't want to appear as?
You can't have your cake and eat it. You're adamant about going against the grain here (again, I'm not saying you're in the wrong, but you are going against the company grain), which effectively pushes back against your company's expectations of you.
You have no control over how someone chooses to respond to your behavior. Whether they get upset or not is wholly their decision. All you can do is choose your own behavior, and based on what you've said here, your mind is already made up on what to do, and you're not going to bend.
Right now, you have to accept the reality that no matter what you say, there's never any guarantee that you've actually mitigated the social damage from pushing back. We cannot predict your colleagues' behavior any more than you can (less so, even).
But there's still the question of how to phrase this refusal to work during your vacation. There are different routes you could take, but each of them work on different people, and they all have their own drawbacks.
1. Argue the legalities. You're not required to work during your holiday, and they can't make you. So you won't work.
This is likely the most effective way to not actually have to work during those holidays, but the social impact is going to be noticeable. If you use this argument, you're being a stickler for the rules (in their eyes), and therefore will likely be treated similarly in the future.
If you enjoy any loose enforcement of rules in your day to day work life, expect that to disappear, instead being reminded to stick to all the rules as much as you did for not working during your vacation.
2. Argue the subjective personal side. You really want this holiday to relax. You'd prefer to not have to work as it detracts from your relaxation.
By opening this up as a discussion, rather than you telling them how it is, you're going to significantly decrease the defensiveness from their side. This might be the right way to sway certain people, who are trying to be polite and won't intrude further when you've expressed a genuine feeling.
On the other hand, you open yourself up to people outright disagreeing with your need for rest, instead pushing through and hammering on about what they care about (problem X, which needs answering).
This approach comes on softer and minimizes the impact, but opens the door to unwanted discussion.
3. Do not pick up the phone or respond to messages at all.
This is again a very effective way to not have to deal with work. If your local culture has reasonable worker protection, no one can force you to work (based on your adamant position, I infer that this is the case for you).
This also puts the onus on the other party, who has to actively engage you to complain about your unavailability. This gives you the conversational advantage, as you can just repeatedly point out that there is no expectation of availability during vacation.
Don't focus on whether you saw the messages or not, because that is not the point. Act as if it's an unspoken but commonly understood truth that one does not work during vacation. This puts the onus on them to explicitly argue that you should work during your vacation, which is a shaky argument from the get go.
However, this is going to rub some people the wrong way. The kind of people who don't deal well with being ignored, or who feel personally insulted by you not catering to them.
My personal opinion is that these kinds of people are liable to dislike you for anything you arbitrarily do in the long run anyway. If you're damned and you do and damned if you don't, then just do what you want to do and be damned anyway.
4. Lie about not having been in the position to respond
This is a more ironclad position than number 3, but it plays out the same way. You simply add an additional argument on top: you were unable to respond, rather than unwilling.
This will help a lot with negating the social impact. Coming across as unwilling to help (which, in truth, you are) is going to reflect worse on you than not being able to help. It also helps with the argument that your vacation comings and goings should not be dictated by your company/colleagues.
However, this cuts both ways. If you act willing-but-unable (to avoid the repercussion of being seen as unwilling), they may outright ask you to ensure availability in the future, at which point this scenario repeats and you've lost the ability to claim that you were unavailable because you weren't expecting calls.
5. Turn it around on them. Would they appreciate being called during vacation?
This doesn't need to be an explicit question; just find a way to make them consider being in your position, being called during holiday.
This is a very useful argument, though risky to use with a certain kind of selfish person.
If this person genuinely believes that employees should remain available at all times, you will damage yourself using this argument. They'll just outright state "yes", and put you on the back foot.
If this person is known to willfully lie to get their way, they will say "yes", putting you on the back foot, even if they won't end up liking it when they are the one on vacation being called.
But if you're dealing with someone who is genuine (not known to lie for personal benefit) and doesn't generally break the work/life boundary for themselves; then it's possible that their current call is nothing more than forgetting to realize what being called during vacation means to you.
While it seems like I'm having to add a lot of ifs here, the reality is that most people are like this. Most people don't mean to barge in or override your vacation. They just honestly misjudge the importance of their problem versus the impact on your vacation, and a gentle reminder often gets them to realize their mistake.
Anecdotally: this approach is actually a great tip if you work in a call center and are trying to finish a conversation because there are other people waiting. We were trained to state "I am going to end this call, because we have many of your colleagues queueing". Pointing out that there are other people (equal to them) being forced to wait, makes most people think to themselves "oh, I wouldn't like to be queueing either, that's a fair point".
But, sad to say, there's always the occasional caller who responds much more selfishly, along the lines of "F** them, it's my turn now!". But they are a tiny minority.*
In all cases, pick your argument based on the person you're talking to.
In the end, different arguments work on different people. There is no one-size-fits-all panacea that convinces and pleases everyone. Some people will be easily convinced, others might never agree with you no matter how well you argue your point.
Over all, before you decide on how to approach this, you need to decide where your priorities lie.
If push comes to shove, and you either have to end up working during your holiday or rubbing people the wrong way, which will you pick?
If you prioritize the not working, then you can speak considerably more assertively when telling them "no" when they call. That doesn't mean being rude, but rather treating your unwillingness to work during vacation as an immovable fact. This gives considerable weight to your position.
However, if you would rather end up folding instead of rubbing people the wrong way, then you're going to have to take a much softer stance on arguing why you shouldn't be working. This is going to smooth the transition to (potentially) having to fold, but it comes at the cost of undercutting your position in the discussion.