You cannot continue to rest a case.  Once you rest your case, you have concluded.
Why they remain republicans is complicated.  I know some who are trying to fight the current trends.  Others remain because they buy the fear being peddled.  Some feel they have no choice because the democrats take positions they oppose and then declare that all who do not support those positions are evil and bad.  When the other side declares your side evil, people tend to entrench.   Personally, I don't see either side as being particularly devoted to the ideals expressed by Christ.