Are Immigrants Government Agents?

I recently realized that conservatives seem to be more accepting of a relaxed policy on immigration when there's a Republican President. In my humble opinion, this makes absolutely no sense. Wouldn't it make more sense to support government activity when one of yours in charge of the government? The only way this even comes close to making sense is if you either assume that immigrants are government agents or if you assume that immigration is a matter of people being forced into the US at gunpoint. (The latter was public policy prior to 1808, so it's only 99% absurd instead of 100% absurd.) Can anybody else explain this?