If private schools aren’t allowed to reject students with disabilities, does that mean they’re legally obligated to make their campuses physically accessible to those people?

No – there’s a lot of wiggle room between “you’re allowed to attend school here” and “we’ve built elevators and ramps and such so you can physically access all our facilities.” Ask literally anyone with disabilities and they’ll give you a million examples.

This is neither here nor there. How private schools feel about a law has no bearing on whether or not the law applies to them.

If (C) is true, the author’s conclusion must also be true.

If private schools are places of public accommodation, then the law (that says places of public accommodation have to [build ramps and such]) applies to them. That means they’re gonna have to [build ramps and such].

(D) reads a bit like a necessary assumption, or just a complaint about the law. Like “hey lawmakers you’re assuming we have the money to even do this!”

Evaluating it as a sufficient assumption, though, just knowing private schools can afford to [build ramps and such] doesn’t guarantee they’re legally obligated to do so.

I mean… I can afford to buy 100,000 pencils. Am I therefore legally obligated to do that?

With some changes, (E) could be right:

Private property is [always] considered to be [a place of public accommodation] by [the law].

Each of these bolded changes replaces a term that kills (E). “Often” leaves room for private schools to be an exception to the general trend. “Public spaces” aren't necessarily places of public accommodation. The opinion of special interest groups is not the same as the scope of enacted laws.