Also, there are plenty of space companies that aren't in the US/UK/China who are hiring (and more willing to work with non-domestic employees since they're playing catch-up), and plenty of companies in US/UK/China who employ contractors that aren't subject to the same hiring restrictions as the first-party/defense-contracted company.
There are a lot more specialized/high-expertise roles here than the ones critical to a nation's space program (or fungible with making weapons). Random examples off the top of my head include crew/life support expertise, launch facility engineering, LEO consumer telecommunications, and more. Space hasn't been fully commodified/detached from government interests--not by a long suborbital burn--but it's moving that direction enough to thaw out the ability to immigrate for work a bit.