Meanwhile, the people in tech who oppose immigration often do bring up the same argument you do - that it's bad to allow immigrants to compete with blue collar American citizen labor even if this competition would make some things that these white-collar tech workers buy cheaper - or ground their opposition to immigration in negative effects of immigrants on American society that aren't directly related to competition for blue-collar jobs (generally, that the presence of large numbers of immigrants has bad cultural or political consequences for the US as a whole).
The political fight over immigration among white-collar tech workers I think has more to do with battling moral claims, or different visions of what the US should look like culturally and politically, than it does over purely-materialist job competition concerns that they are hypocrites about when the job competition is happening to blue-collar workers.