Billionaire hedge fund manager Paul E. Singer is one of the Republican Party’s most important money men, raising millions for presidential candidate Mitt Romney and giving even more to a super PAC supporting his campaign. But Singer is also a longtime backer of marriage rights for gay men and lesbians, putting him in stark conflict with Romney and the Republican establishment. The contrast underscores a growing rift between the main Republican Party — which reiterated its support this week for a constitutional amendment banning gay marriage — and a small group of conservative donors who view the issue as a matter of individual civil liberties. Singer has given $1 million this year to Freedom to Marry, a national bipartisan advocacy group focused on winning state ballot measures on marriage in Maine, Minnesota and Washington. The group plans to spend at least $3 million on its efforts. Singer, founder of the $20 billion Elliott Management fund, also gave $1 million in start-up money to American Unity PAC, a new super PAC focused on supporting Republican congressional candidates who favor marriage equality.