It seems to me that "are against immigration" means multiple things that are worth separating. If "old Republicans are against immigration", that might mean

• that when asked their opinions, that's what they say
• that when given the choice of voting for anti-immigration Republican candidates or pro-immigration Democratic candidates they choose the former
• that when given the choice of anti-immigration Republican candidates or pro-immigration Republican candidates they choose the former
• that when they have the opportunity to influence Republican party policy they try to push it in an anti-immigration direction

and these are all different things.

Voting mostly for reasons other than affecting the outcome certainly explains the second of those, but that one wasn't particularly in need of explanation anyway if Republican candidates generally suit the self-interest of old Republicans better than Democratic candidates.

(Perhaps your argument is that actually voting Republican at all is against the self-interest of old Republican voters? If so, it seems to me like more support for that claim is needed.)

As for the others:

• Stating "immigration is bad", like voting for anti-immigration candidates, doesn't actually have much likelihood of changing immigration policy, so maybe your explanation also covers that (and, more generally, pretty much any expression of political opinions). What it doesn't explain is why those old Republicans would want to say that immigration is bad; an obvious explanation (which again generalizes to wealthy Democrats advocating tax increases, etc.) is that they consider their interests advanced on the whole if their party does well, and so they advocate for all their party's positions.
• Do we actually know anything about what old Republicans do when they have a (real) choice between two Republican candidates who differ mostly in immigration policy? (To whatever extent e.g. Donald Trump is a particularly anti-immigration candidate, his success in the Republican primaries might be evidence, but it feels like there are way too many other confounding factors there.) My impression is that there just aren't very many pro-immigration Republicans around to vote for.
• Do we actually know anything about what old Republicans do if and when they have a chance to influence Republican immigration policy? (My impression is that most old Republicans have no such chance, and those who do might be highly atypical in various relevant ways.)

It turns out people are complicated.  Huh!  And representative democracy (where voting is for people, not policies) plays into this BOTH by triggering social-judgmement modules of like and trust the presentation of the person, without regard to policy behaviors, AND by combining policy choices in weird workshopped compromise bundles.

I'm kind of sad Robin Hanson has moved away from "signaling explains everything".  It's not literally true, but it's far more true than analyzing any behavior without considering the association and cultural signaling aspects.  This isn't necessarily literally trying to show others something, but very often self-signaling - showing yourself what you'd like others to see.  

"Explaining" why your political opponents hold views that "harm them" is disguised Bulverism. As a human, you are not that good at determining that your opponents are wrong. No, not even if you start your post with a perfectly logical description of how there's no choice for any rational person other than to agree with your political side.