I'm posting while deliriously tired so when reading please factor that in.
A 504 is a set of necessary and appropriate accommodations for a student on his/her behalf is to remove a barriers to education.
The school imposing a policy of isolation/segregation based on disability is restrictive.
Tying one to the other is disability harassment. It forces a false dilemma on parents, strong-arming them to accept social isolation in order to receive an accommodation.
Ask for an excruciatingly detailed explanation how they arrived at the conclusion that they can provide conditional accommodations with strings attached when the prohibition on disability always favors greater protections with the least restrictions. And, how they have concluded that a school policy can overwrite federal law. Sources cited, etc.
^The above needs some work over from the others here, although I think we're all in agreement here no matter how differently we express it. I think you need some backup in the form of sources to cite. Some paper to hand over like, yo, deal with this federal law, department or something like that.
Best guess? The school thinks it found a loophole. It's a rather mean spirited one, IMO. So beware that it could be a few snaky administrative persons you're dealing with. I'm not sure they can be reasoned with but that's all speculation. You still got to try.
I'm not sure the best approach is arguing the lunch room versus classroom as the underlying point, because that might be a way for them to get you hung up on the ropes, tire you out, on a point they feel strongest about. The underlying matter is accommodation versus imposition and the harassment for seeking an accommodation they don't like. Strike at the heart not at the feint.