How to push back against feedback that is generally unfair and hurtful?

Zooming out, I recommend not worrying about problems that don't exist (yet). Getting hurtful feedback is a sad thing to think about (and not very likely if you follow the Taro advice of building relationships/doing good work), and putting yourself into that negative mind space increases the chances of a self-fulfilling prophecy (i.e. you're in a bad mind space -> you don't work well with others -> you get bad feedback).

Should I just document everything?

Yes, always be trying to create artifacts from well-documented pull requests to system design documents. Having an extensive paper trail not only helps you with promotion, but it also comes in handy if you need to defend yourself.

To answer the original question, it's almost always wrong to push back against feedback, even if it's incorrect. The main misconception people have is that they think what's important is whether the feedback is correct or incorrect. This is entirely untrue: The important part of feedback is the intent. This is why feedback is so nuanced:

• A well-intentioned person can deliver feedback that is incorrect
• Feedback can be sort of correct and incorrect at the same time (e.g. you get feedback that you should speak up more in meetings and you do speak up in 70% of meetings, but there are 30% where you're completely silent and those are the ones your manager is in)

If the intent is bad (they are just delivering fake feedback to insult you in a weird back-handed way), then you have a bigger problem. If they're in a position of power, you probably need to change teams. If they're not, rope in your manager. But again, it's strange to use feedback to sabotage someone. If you wanted to hurt someone, it's better (and easier) to be low-key about it and try to get them PIP-ed behind the scenes.

• Keep a "job diary" of the feedback you receive. Since this is private, just write everything down without filtering, and how you feel about it.
• In your manager 1:1, take some time to reflect on the feedback and present a plan on how you're addressing it, and what you'll do differently for future feedback.

If you feel like the feedback is unfair, my recommendation is to be curious. Instead of being defensive, ask for examples and genuinely try to understand. After the dust has settled, you can provide "feedback on the feedback" if you feel like it was too personal/insulting.