The two "insanities" are not mutually exclusive.

In fact, I agree with you that illegal immigrants abuse the system and unfairly consume resources. I also agree with the parent comment that people acting as a police force (i.e., ICE) should carry and present ID.

As a legal immigrant who waited years to get my citizenship lets point out that most of those immigrants actually pay for the same programs too, though not always "in their name". Undocumented immigrants still pay tax and deductions on their paychecks, too.