Seemed to manifest as a pretty consistent pattern in about a dozen playthroughs, though granted, it was far from the only secondary preference they had and NatSec was more common. In general, though, I was able to have multiple nativist virtual voters in the front rank of my supporters while doing pretty radically pro-immigrant things provided I did enough pro-worker and pro-socialist things, which doesn't strike me as being how nativism works at all.
(In general I have questions about nativist voters *allowing* secondary priorities to overrule their nativism in the environment being simulated, but that's a larger question.)
It's not a deal-breaker. Just something that put me on notice about certain ideological things going on. I still had fun.
That might be because some options, like the "hope" inauguration speech and canceling student debt, have universal appeal -- maybe you managed to get them on that? But I dunno, I don't think it's too unreasonable for people to be swayed by policies that directly benefit them even if they disagree with ideology -- on the flipside, look at all the rural voters who said they disagreed with Trump's nativist rhetoric but voted for him anyway in the hopes of restoring the economy.