The funny thing is that the groups that actually make up the democratic coalition are opposed to one another. Should the GOP go to demographic ill-relevance, the Democratic party will likely splinter.
Hispanics and blacks are at odds with one another for jobs and public resources. Hispanics have pushed blacks out of some of their historical neighborhoods.
Women's rights are at odds with muslim beliefs.
Asian's are at odds with other non-white demographics over AA admissions and democratic economic policies run counter to asian entrepreneurs.
Gay rights are at odds with hispanic and black religious beliefs.
The Republican party has the perception of being the party of white people, largely because they are indifferent to minorities, not because they advocate for whites. Its not like they are going to embrace being the white party because they are afraid of being called racists. A clever Republican politician could play those democratic groups against one another, but would probably take a lot of heat for doing so.