FR TP flop

You should answer this question before you decide to call: will you call another bet on turn?
If not - then fold.

I would fold here as well. We don't have enough equity to call 2-3 streets and we can't have a T♥: here. Just live to fight another hand

Calling flop doesn't commit us to call turn. I'm pretty sure it is game-theoretically correct to call flop and fold a (very small) part of the range. (That part depends on the turn card of course.) This is a hand that could belong there.

That said, if you for some reason know that you are folding and you really know that a turn bet it coming, then fold right away. This is exploitation (and hence exploitable).

As always, it really depends on the Villain. I personally think that calling the flop and folding on turn can be OK, as long as you have some sort of read (maybe Villain is aggressive, bluffing a lot) + you will have position on Villain on future streets. Often people will try try to c/r the flop to scare you off the hand and will give up on the turn. If they keep betting, they usually "have it" and you can safely fold. That said, if Villain is very tight, just fold and be done with it.