I think I see where you're coming from. To use an example, Switzerland has tight immigration controls due to the policies which grant citizens and permanent residents certain welfare benefits, since they don't want those to be leeched by people who do not contribute as much back. That is against immigration while not being anti-immigrant; the point is that the immigration itself does not motivate the policy which limits immigration, instead being motivated by the existence and meaning of other policies (a kind of protectionism).

Tying this back to OP's comment, it's hard to see these policy changes as any sort of legitimate protectionism and it's just as hard to divorce them from the justifications given by people who start with "I'm not anti-immigrant".