I'm a female engineer who has worked in male-only teams for many years and heard words like "man-hours" many times. Among the great answers here, I don't see my view on this represented, so perhaps I can add something more.
Is this usage appropriate in the workplace (and I should accept it),
or would changing it at my workplace be feasible? Is there a better
term to use?
In the first year of working, I learned a very important lesson. If you do good work, it doesn't matter what gender you are, you will be respected. It begins and ends with the quality of your work and your attitude while doing it.
With the above in mind, there is no need to draw attention to your gender. It doesn't matter if you're male, female, or non-binary. I don't draw attention to my gender because it shouldn't play a role at all in my work life.
I do not wish to be treated specially (good or bad) due to my gender being different, so I don't want to draw attention to it, and I don't want to draw other people's attention to it.
So, going back to this:
would changing it at my workplace be feasible?
You would be asking people to pay attention to the fact that you're female, and treat you differently because of it (changing the words they use). This is something I personally wouldn't do.
There have been times where people have said "woman-hours" instead of "man-hours" for me, and I specifically don't like it when they do that. I usually say "no need for that, really!" in a joking kind of way. Why? because I prefer being treated like everyone else. And if everyone else gets "man-hours" then I should too.
I don't want the people on my team to think twice when they talk to me. I want them to be comfortable. I don't want them to walk on eggshells and feel like they could offend me at any moment. I'm here to work, not make them uncomfortable or make their lives difficult.
The majority of the men I've worked with have been absolute gentlemen toward me. I have been respected and treated very well on the teams I have worked on. I understand that some women have not had as good an experience as I have in the past.
If you are not being treated well, or respected on a human level, then there's nothing wrong with raising an issue and talking about it. I don't mean to let people walk over you and say what they want to you. My point, rather, is that this is just a matter of semantics rather than anything else, and that I personally would just let this go and appreciate that you are being treated the same as everyone else.
A couple of people have indicated concerns about this view being too passive and just accepting male terms as default.
I agree that words are important. I agree that ideally words should be changed. There is nothing wrong with advocating the change of language. My argument here is to say that actions are more effective than words. A man can say "man-hours" and it has no indication of his view of women, sexist or otherwise. English evolved over centuries and it's not going to change overnight any time soon (there's nothing wrong with trying to change it, though).
The real trouble isn't with the words, it's with the mindset that women are inferior. That they aren't clever enough to be engineers and do good jobs, that they have only specific roles in society to fill. Now obviously not all people feel this way, but some do. And if you show that you are a good engineer, that your gender does not affect your work standard at all, then that is much more effective than changing how people address you.
So there is nothing wrong with switching terms and using another word yourself. However, if you want to change others, your actions are going to be a much more effective influence on their mindset than asking them to use a different word.