What that Yoda guy said
I think one flaw in that question is that most of those who oppose immigration also don't see themselves as coming from a family of immigrants, they're most likely at least 3rd generation Americans, and though they come from a family of immigrants it's far enough back that they may have not even have met that 1st generation. This then puts them in a place of privilege not knowing the struggles of those coming to America from around the world who aren't as fortunate as them. A lot of people in the previous posts talk about being afraid of immigrants and I'm inclined to agree, not only does the privilege not allow them to emphasize with immigrants but also make them want to retain the status quo, because if you're privileged why change that? I personally fear a change in the status quo with some things (college) so I can kind of relate (not really though). This fear influences their view and skews it, let's say you're a coal worker in let's say West Virginia how likely will an immigrant willingly move to West Virginia of all places to take your job, short answer, it won't happen but that fear that it COULD happen drives people to oppose any immigration especially from the southern border. That fear then becomes anger, as they see their job being taken when the coal industry fails because there's no more coal, it then transforms into hate because nobody is actually at fault but when nobody is at fault it's unsatisfying. So when a loud "politician" says it was immigrants who took your job you're inclined to believe them to take out that anger.
There's also a fear of losing the "American Culture" which translates out of dog-whistle into "White Culture". I remember seeing a headline from Fox News that read "surprising demographic changes that we did no vote on" they then went on to discuss America becoming more mixed as different races intermingle and I was honestly in shock, that line had to be okayed by at least three people and it's such a blatant push towards either the government controlling who has kids with who (which Fox wouldn't say) or to stir up fear of losing White Culture. I again get the general idea of what they want cause I don't want to lose my culture but again where most of these people live, their culture won't be changed by immigration for a very long time.