We do screen legal immigrants. I sponsored my ex-husband (he was then my husband) for a green card and he had to be screened (like other immigrant visa applicants) for HIV, tuberculosis, etc. He also had to prove his vaccinations were up to date or have them re-done. He was also subjected to a psychological examination.
Visas are routinely denied on medical grounds. There are entire web forums devoted to griping about the legal immigration process.
Been there, done that. Ask me anything. If I know the answer I’ll share it. I’ve also been a (legal) immigrant myself so I know the process in the UK too.
Thanks for the info.