This feeling of not belonging extends to people who, nominally, should be on the other end of the desirability spectrum.

I used to work in the United States on an H1B visa. The terms of the visa are that employers are legally required to ascertain that no US citizen is available to do the job for which a H1B is being hired. In effect, the H1Bs you saw around you were DEFINITELY needed. They had been vouched for under law by the organization where you saw them

We still felt this scarlet letter of stigma hovering over us. We were like Schrodinger's immigrants - wanted and not wanted in equal measure.

Not sure if this comment adds to the conversation but it happened and it is probably happening around us right now that people are feeling unwelcome and judged. It is not a pleasant place to find oneself.