Immigration isn't a "new" issue. Besides its more likely the GOP moderates on issues like LGBT rights and birth control than immigration at this point.
Again, We have had the same immigration policy for 50 years with "Taft-Hartley". What's there to moderate on on that issue unless you are talking about an immigration reform package passing through Congress?
Birth Control-Its the Democrats that are fighting about abortion currently not the Republicans.
LGBT-Can you be more be more specific?
Taft-Hartley is the trade union law and has nothing to do with immigration.
And by LGBT I mean I can see the republicans abandoning its support for things like bathroom laws and its opposition to transgenders serving in the military.