1. The laws against marrying a first cousin, as well as polygamy, probably are unconstituitonal as they are both based on canon law. How legalization of polygamy will affect us is open to debate , but many hold that the halachic ban doesn’t apply in countries in which polygamy is legal.
2. While we have never followed the goyim’s laws in such matters, many of the Christians who lack a canon law tradition (e.g. Baptists, Mormons, and most fundamentalist Christians) always held by the government law in marriage matters, and will be forced to create their own legal rules, and will seek to have American return to a system a personal law (common in much of Africa and the MIddle East, but abolished in America and England roughly 200 years ago).
3. The dubious practices of the goyim aren’t really our problem. Its not like they were especially know for their chaste behaviors previously. The real change to marriage law came a century ago when they decriminalized non-marital intimate relations, which had previously been illegal.