with more ‘liberal’ types I have to suffer a different kind of rejection wherein it is denied that my issues qualify as oppression because there are simply limits to what any one liberal is educated on.
For what it's worth, that's a very specific form of oppression that folk in similar positions uniquely have to deal with.
I'm a cis passing trans woman. People don't realise I'm trans unless I tell them, which means I don't deal with the overt transphobia many of my peers do. But I still deal with it when I come out to people, and when viewing the hate and bigotry that target us. I still internalise all of the crap that society flings at us, and unlike an actual cis person, my "privilege" can evaporate in an instant in some circumstances.
As for how you deal with it? The way I deal with it is to acknowledge that I do face less extreme bigotry than many of my peers. That is true, and it needs to be acknowledged when talking about my lived realities. Yet at the same time "less bigotry" isn't the same thing as "privilege". It's a discussion you can have with folk that are open to nuance, and it's not one you can have with folk who aren't, even when they're ostensibly allies. That is, unfortunately, part of the package :\