Assume villain is playing a 100% 2x strategy. You are big blind, assume you can't 3bet and can only check raise on the river to make things simpler.

Let's say we defend just the MDF vs this raise size which is 50%. So we get to the flop with the top half of the hands we have preflop. Villain cbets the flop POT, and we defend the MDF again, which is the top half of the range we get to the flop with. He pots turn, we defend the top half again. And he bets POT on the river and you also defend the top 50% of hands (this time defending by calling, value check raising, and bluff check raising to hit the MDF).

In reality, some of the weaker hands still have enough equity vs a 100% range that villain is opening to call more than 50% if we can realize enough equity with these weaker hands given the pot odds preflop, then we should call more than the MDF preflop.

Let's assume we VPIP 85% of our hands vs the 2x raise. Do we still have to call the MDF on the flop vs a cbet or is it okay to fold some of our trashier non-connected hands that don't hit the flop even if it makes our calling frequency less than the MDF.

TLDR: If we call more than the MDF preflop because we are laid good pot odds, is it okay to fold more than the MDF to a cbet? Can't villain exploit us by cbetting any two cards on the flop if we fold too much?