The movement to grant immunity to illegal immigrants is both ethical and pragmatic. Ethical because illegal immigrants who have been present in the US for more than a decade (more than half of them!) are de facto Americans, and it's wrong to deport Americans. Pragmatic because there's millions upon millions of them, and any deportation effort will be both very expensive and sure to accidentally sweep up some legal Americans.
Conservatives often pair this grandfathering-in with increased border and interior security. This is at least a thoughtful and consistent response.
The idea that Democrats have consciously decided to "annex" Hispanic votes gives far too much credit to the Democratic party: the hostility of Republicans explains Hispanic voting patterns much better. For example, in Florida, there are 40% more unaffiliated Hispanics than Republican-registered Hispanics [1].
[1] http://www.pewresearch.org/fact-tank/2016/03/09/democratic-e...