WIC is funded by the Federal Government and use US tax money to fund it. Also, illegals in all States use it. It's a Federal handout, the States just set the income level cut off, and of course, they use Federal paid for studies to set those levels.
I don't see the connection to the other two. How do Illegals benefit from those programs.
They get Federally Insured, cheap home loans. And yes, they do use both.