How would a renter feel if their rent increased because their landlord was unable to take a mortgage deduction? In other words, is the deduction implicitly distributed pro-rata to the supporting renters via market force?

In the US, the home mortgage interest deduction does not apply to rental properties. To qualify for the deduction, you either have to use the home as your residence for a minimum period each year, or rent only part of it (and meet requirements for renting part of the home: you can't have more than two tenants, and the part of the home they live in can't have its own separate kitchen or toilet facilities).

But that's the home deduction. Apartment buildings, for example, are investment property for which mortgage interest is a deductible expense. https://www.irs.gov/publications/p527/ch01.html

Then you concede that taking away the home mortgage interest deduction (making the homeowner-who-resides-in-the-owned-home and the renter equal for tax purposes) would not drive up rents, and your original comment was at worst wrong and at best a non sequitur.

I'm positing false equivalence. Taking away the home mortgage interest deduction would make the homeowner and renter unequal. Doing so would not drive up rents, just as eliminating the mortgage deduction on investment property wouldn't impact house prices.

You said:

How would a renter feel if their rent increased because their landlord was unable to take a mortgage deduction?

I countered that the home mortgage interest deduction doesn't apply to rental properties. Renters and homeowners are thus currently unequal from a tax standpoint, since renters effectively pay a higher tax rate than homeowners. Removing the deduction would thus not create a new inequality; it would remedy an existing one.

The home mortgage interest deduction specifically doesn't, but mortgage interest on rental properties is still generally deductible.

https://www.irs.gov/publications/p527/ch01.html

I wholeheartedly disagree.

If I choose to live rent-free in my parents' basement, I will not get fined for doing so. I keep ALL of my cash. But I'll STILL get fined for having not buying myself insurance.

I'm not sure what logical fallacy you're throwing here, some form of "Denying the antecedent" or something along those lines, but it's not the same situation.

In both cases, A does something and B does not, and the result is B pays more income tax than A despite A and B having equal income.

Why people insist the two cases are conceptually different (i.e., that one and only one of them is a "fine" for not doing the thing), I do not know.