It is a sensible combination to me. If you first believe that the government should provide a bunch of free stuff, but it doesn't at the moment because it's too expensive, it kind of makes sense that you would then think there need to be fewer people getting the free stuff so it remains affordable. The first people on the exclusion list would naturally be noncitizens.

You can exclude people you don't like from free healthcare without physically removing them from the country.