If it came down to separate countries for the purposes of avoiding a civil war, many white libs would align with the minorities. But after about five years a very large pct. of those white libs would be pounding on the border wall, begging and pleading to be let back into the conservative country. Within a very short time all white libs would discover that they are just some other white people who would have many laws passed discriminating against them. Think Zimbabwe and South Africa. That's if their entire wealth was not outright confiscated (likely) by the new rulers of The Socialist States of America.
I would not put some kind of racial litmus test on who could live in the conservative country. All people of any ethnicity would simply have to vow to abide by the principles of the constitution. No favors to any ethnic group. Any group or people trying to seek special favors due to their race or ethnicity would be escorted to the border and thrown over the 100 ft high wall separating the countries.