I don't think it's "catering to them" to avoid passing laws that impose undue burden. For example, if you passed a law requiring a US passport to buy food in the US, and made it so all restaurants and grocery stores are required to check passports before selling food to anyone, I would be opposed to that law, and part of the reason is that I don't think it should be hard for anyone to get food, whether they have a US passport or not.

"Undocumented" doesn't mean "residing illegally" anyway, it just means "lacking documents", which is a state that many perfectly legitimate US citizens find themselves in. But we should want people who are here illegally and everyone else to be able to use the world wide web and computers regardless of their legal status, just like everyone should be allowed to eat and buy food regardless of their legal status, because that's just basic humanity.