Earlier quoted context omitted.
Biases, prejudices and so on are subtle and take a while to unlearn. If you want to get rid of them, you essentially have to interrogate your own thoughts, for better or worse. If you're not conscious of a bias, you can't get rid of it. It doesn't suck the fun out of life.
I'm not sure how your parent even jumped to talking about "political correctness" in the first place, since that's not at all what the article meant by "right" thoughts and feelings. But you're spot on. It's difficult to unlearn something that you never knew you were learning in the first place, because you just take it as fact or how the world is. Confronting your own biases is uncomfortable, but it's well worth it,…
It's funny to me, since I do, to some extent, try to recognise my prejudices in my thoughts, but it's not been a problem for me. Whereas I actually have had problems with worrying about whether my thoughts and feelings are “right” in the sense that the OP is talking about.