I put more thought into this topic than I should.
For the most part (a.k.a. most OLL's, PLL's, and F2L algs) I use my right index finger for F, and either my left index finger or my left thumb for F'. I found that Collin Burns constantly uses left thumb for F', especially during F2L. His
F2L algs video shows him doing this quite a bit. Obviously, it's better to use left thumb for simpler finger tricks, like The F' on a T-Perm or a J-Perm. It felt kind of awkward at first, but I've gotten more comfortable with this over time, especially after learning algs/incorporating fingertricks that included F2, as it's actually pretty easy to double-flick an F2.
For 3x3, I've personally found doing F' with your right thumb (by pushing upward or what have you) ruins the fluidity of the solve, whereas doing it with either your left thumb or index retains fluidity. For big cubes, however, I've found that using right thumb for F' (especially for certain algs, like the F' at the end of a Y-Perm) keeps the cube more stable and makes it easier to hold while still executing with decent TPS.