First, you have to accept that if you are doing your job well, then your work makes others look bad. That is nature of what you do and you cannot compromise that in order to maintain friendly relationships.
So first accept that you are not ever going to be popular.
However, that doesn't mean you can't be respected.
To do that, first be absolutely sure that you are right when you criticize the practices of others. Every time you are right, you gain credibility. When I worked for an audit agency, we almost lost a political battle on a major multi-million dollar finding due to a rounding error of a couple of cents.
Next, you need to listen to their responses and see if you can find something you can agree with. If you were wrong and they pointed out a valid mitigating factor, then you will be better off to agree and go from there. This doesn't mean change everything due to what they say in response, that is a bad thing. But when they are right and you are wrong, you have to admit it and change the finding. You will get respect because you listened and you admitted to a mistake rather than fighting tooth and nail to avoid admitting a mistake.
If you balance reports by mentioning things that you found that they did correctly, that helps too. Also, you may need to talk to your own boss about whether something is minor enough not to be brought up or when it needs to be brought up. People have more trouble with auditors who find only picky ridiculous things than with auditors who find genuinely major problems. Your organization will have its own standards on what needs to be in the report and what might be communicated informally. Your boss should give you guidance on this. If possible concentrate the most time and effort on major issues.
Now of course, you will always remain cordial and professional when talking to others. But truly you do not want to make friends with people outside your department who you may audit, that is a conflict of interest. If you are friends with Joe and you audit his group and he is the only person who doesn't have many issues, are they going to assume that his friendships is why you were easier on him? Best not to go there or you may end up either destroying your professional credibility or losing a friend.
You also have to develop a thick skin. Yes they are going to disagree and they may even say not so nice things about you. You have to rise above and not respond in kind. You have to understand, they are not mad at you as a person but at your job function. I had to learn this early on when I was a manpower specialist (people don't like being told they need fewer people either!) and it has served me well through the years. If you are in a not popular job, then negative reactions are part of that job and you have to learn to not let them get to you. It becomes almost a badge of pride that you found something major enough that it made them mad.