Make their spouses lose their job for being an ICE spouse

I suspect a non-trivial percentage of the spouses may be victims in abusive reltionships - the loss of employment could make it harder to extract themselves and their kids from the situation.

make their kids ask uncomfortable questions.

as long as the kids are not harrased and they start asking because daddy is a piece of shit? 100% 👍

Make their neighbors avoid them

ab-so-fucking-lutely!

eyeballs that can be verified remain important, yes. however, privacy and pseudo-anonimity are equally important.

most sites use JavaScript to restrict access. Firefox (or its siblings) extensions like noscript are not only useful for bypassing many js walls, but also for general web hygine. noscript is your friend.