If you don't want an "illegal immigrant" on your private property, that's your right. You can exclude anyone just like you can invite anyone (including those government forbids you to invite).
I'll never understand how anyone imagines they can tell someone's "legal status" without checking the government paperwork and being a lawyer, but whatever.
I may think you're a jerk, depending on your choices, but I'm not going to try to force you to allow just anyone into your home. You have every right to be an unpleasant hermit.
If, however, you have a store that is open to the public and you say "illegal immigrants" aren't welcome, I think you're in the wrong in more ways than one. Maybe you don't understand what "the public" is. If you have a store that is open to the public, there's a presumption baked in that people don't have to wait around outside your door to find out what exceptions you impose.
If you want to exclude some people, based on anything other than archation being committed right now or the credible threat of it being committed while they are in your store then don't invite the public.
If, instead of being open to the public, you want to have a "buyer's club" sort of thing and access is granted to members only, and you choose who is allowed to be a member and who isn't, that's acceptable. I doubt I'd join, but you do whatever makes you happy.
That's different than letting someone force you to provide a service you don't offer. I don't think it's right (or sane) to force someone to "bake the cake". Who would be stupid enough to consume food or drinks prepared by someone who is doing so against their wishes? Not me! That's completely different than buying a sock from someone who doesn't like you.
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