does MDF really matter? lets sat vs a 75% bet you have to fold 40% of your range? what if 80% of your hands have enough equity to call? would you still fold out those high equity hands or stick to MDF? or what if your hands in your range don't have enough equity to meet MDF? what happens then?

You can call over mdf if your hands have the equity to call however your opponent could exploit this by never bluffing.

If you call at mdf you're making it difficult to exploit your calling tendencies. You're calling just enough to make your opponent's bluffs indifferent to betting or checking while you avoid over paying off the value portion.

Edit: I should note that personally I think MDF has limited utility outside the very strict parameters of the toy games that illustrate it or scenarios that closely resemble that in real games. So I wouldn't strictly adhere to mdf while you're playing more of use it as one point of information to take into consideration while you're making decisions.

You seem confused. MDF has nothing to do with equity. Are you referring to pot odds?

? Sure it does. If you face a bet you have to have enough equity to call. You never defend hands that don't have enough equity to cal vs the bet size you're facing.

You're describing pot odds. Pot odds tell you how much equity you need to call a bet.

Minimum defense frequency, or 1-alpha, simply tells you how often you need to defend to stop villain from auto-profiting with a bluff. MDF has nothing to do with equity.

For example, if I bet 10 chips into a pot of 10 chips, then your MDF would be 50%, but your pot odds would be 33.3%. So ideally, you'd want to continue at least half the time with hands that have at least 33.3% equity.

But in practice, you're often going to get a mismatch. Sometimes you just won't be able to defend wide enough, and other times you'll be able to defend much wider than MDF. Sometimes you can call hands that don't have correct pot odds, because of implied odds. Sometimes you should fold hands that have correct pot odds, but poor reverse implied odds. Blindly following mdf/pot odds is not a good strategy.

You have to be able to estimate the equity to have to know if you're getting the correct pot odds. So equity is always a factor. Without estimating my equity I have no way to make an informed decision about my pot odds.

It's not directly related to mdf, but it made sense to use equity in the op when describing portions of his range (i.e. 80% of my range has enough equity to call).

That's fine and all, but both you and OP are conflating the two terms "MDF" and "Pot Odds". To be clear, MDF tells you how often you want to continue, whereas pot odds tell you how often you want to win.

MDF is a pattern that tends to arise on the river if and only if both players are playing close to the equilibrium. It's in the bettor interest that the caller gets a 0ev call, and it's in the caller interest that the bettor gets a 0ev bluff. And mdf is the point where those 2 frequencies intersect. Now, if your opponent where bluffing at a different frequency, should you stick at mdf? Of course not, you should move away from mdf and exploit him.
In other words, if we are at equilibrium, the bettor will give us the right odds to defend at mdf, because it's in his interest. If he doesn't, we are not at equilibrium (or not on a polarized bet type of action where mdf applies)

Or maybe you are asking something different. Mdf only works perfectly in a river situation against a perfectly polarized bet situation yadda yadda. On almost any other poker situation the equilibrium strategy won't be to defend mdf, altough it's very often close and you can even usually modify the mdf formula to better reflect your current situation to get accurate approximations of the correct defense frequency.

Which ones of the two answers is the one you are interested in?

I am not conflating anything.

Op's question put another way without using the term equity is "what if I have more hands in my range that can call but I have more than mdf?" He just went a step farther and said "what if I have more hands in my range than mdf would suggest I need to call with but they all have the appropriate equity to call?"

Pot odds take precedent over MDF

MDF isn't followed generally anyway if there are still more streets to come, or if there is a particularly unfavorable river card, or other dynamics which may cause MDF to be disregarded, even on the river