Adam Ozimek uses my own words against me to defend liberaltarianism from my critique:

I disagree with Bryan’s presumption
that domestic distribution actually encourages that much of a
restriction on immigration, or at least that the immigration
restrictions we have would go away or significantly loosen if we
suddenly abandoned all redistribution policies.

This is because people would oppose immigration pretty much
regardless of how much or how little immigrants benefitted from welfare
and redistribution policies. How do I know this? Well, because Bryan
Caplan told me so. In his excellent book The Myth Of The Voter Bryan identified the anti-foreign bias,
which is a “tendency to underestimate the economic benefits of
interaction with foreigners”. No amount of minimal government is going
to do away with this bias, and I don’t think it will help reduce it
much on the margin either.

Anti-foreign bias is indeed strong and durable.  But this hardly implies that it is invariant to circumstances.  Immigration really was much more free before the welfare state arose.  Welfare state abuse really is one of the most popular arguments against immigration.  And there is good evidence that opposition to the welfare state heavily depends on the perception that out-groups disproportionately benefit from it.  It’s no stretch to flip this evidence and say that support for the welfare state heavily depends on the perception that out-groups don’t benefit from it.

You know why else I think more immigration is consistent with welfare policies? Because Bryan Caplan told me so. In the slides
to the presentation he gave on immigration for the Future of Freedom
foundation, Bryan specifically counters the Milton Friedman’s claim
that “You cannot simultaneously have free immigration and a welfare
state.”

[…]

So Bryan is right and immigrants are net tax payers and they help
spread the costs of national defense around, then more immigrants
should make our welfare state that much easier to maintain.

This depends on the kind of welfare state you’ve got.  When you’ve got one like the existing American welfare state that focuses on the old rather than the poor, then the position Ozimek quotes makes sense.  But if we followed the liberaltarian dream to have “wicked-good social insurance,” I’m afraid Friedman might be right after all.

In any case, the political economy issue isn’t whether immigrants are really a burden on the welfare state, but whether they’re perceived as such by voters.  Ozimek seems to get this:

If an anti-foreign bias prevents people from seeing that current
immigrants provide us with net economic benefits even with our welfare
policies, then it would seem foolish to abolish those welfare policies
on the hopes that it will somehow convince people to suddenly abandon
the anti-foreign bias that prevents them from seeing that they don’t
matter in the first place.

But I’m not convinced.  Even in the face of severe anti-foreign bias, “We don’t have a welfare state to rip off” is a much easier sell than, “We have a really big welfare state and immigrants make it possible.”