There's a world of difference between accepting someone's claims of their experience at face value and accepting that these claims justify the demanded changes.

There's no conflict in acknowledging that someone does hear a high-pitched noise in the presence of a particular device and at the same time do not accept that this would be a sufficient reason to prohibit such devices or turn off a particular device; and at the same time one can acknowledge that the term 'blacklist' is offensive or triggering to some people and at the same time not accept that a term being offensive or triggering to some people is sufficient justification to require the world to change that term.

So if someone says their lived experience is pain and suffering from the existence of cancel culture, you fully embrace that and want to do everything you can to help them stamp out cancel culture?

Or how about this one: what if someone says their lived experience has always been a negative interaction with every member of some specific racial group. You then believe them and accept their racist views as legitimate?

I just can't accept that you actually believe what you are claiming. We all must evaluate and judge so called lived experience on its merit, not blindly accept it as legitimate.

I think you are missing the point, and the point of the original "appeal to politeness" argument. It is polite and appropriate to give someone the benefit of the doubt and "believe them" as in follow their line of thinking and investigate the point of view that they have. However - giving someone the benefit of the doubt and trying to see their point of view doesn't mean you follow their every command and accept every proposed solution. It just means you listen, and try to work with them to solve the problem.

that slippery slope is totally real, unfortunately

It'd be rude to deny you think there's a slippery slope, though I would note that you did introduce that part yourself.