I'm not on the far right, but I can tell you that of those I know who are, precisely none of them are 'anti-immigrant'. The majority of them would like to reduce illegal immigration and improve border security, but that's also true of the vast majority of Americans as a whole.
Perhaps when you say 'immigrant' you are actually referring to illegal immigrants? Even in that case, over 3/4ths of Republicans favor a pathway to citizenship for existing illegal immigrants (including 'dreamers').
[1] Previous Gallup research has shown that 77% of Americans say that "controlling U.S. borders to halt the flow of illegal immigrants into the U.S." is extremely or very important. And 83% favor "tightening security at U.S. borders." http://news.gallup.com/opinion/polling-matters/209384/buildi...
[2] http://news.gallup.com/poll/193817/republicans-favor-path-ci...