So we want to go somewhere that's more affordable

Mhm...

a public transit system that actually gets you where you want to go

Debatable.

I guess my general question is, does it seem like a good time to buy a house in Philly in those neighborhoods or in ones similar to those?

No. Even shitholes in my neighborhood (which isn't even close to being gentrified) are being listed for insane prices. My girlfriend and I have been actively looking for months now.

Fishtown is ridiculously overpriced and Point Breeze is great if you like getting harassed because you're from out of town/stick out like a sore thumb and also probably having your house broken into.

This literally just happened to some friends from college, then everyone on the block who was questioned said they didn't see anything despite it being summer and everyone being outside. I had another buddy who I just helped moved neighbors were threating to kill him and shit, throwing stuff at their house at night, harassing him and his girlfriend when they would leave the house.

do Native philadelphians hate on transplants as much as native oaklanders do?

Probably moreso. The only people that are welcoming to transplants are other transplants and it doesn't take much time for them to start claiming "yeah I'm from Philly" so the cycle repeats. Personally, as a Philly native, I don't mind if people come here as long as they keep to themselves but many do and you will encounter that often.