WASHINGTON — With Virginia’s gay marriage ban overturned, the legal fight over same-sex unions in that state goes to a court that has shifted to the left since President Obama’s election.

It’s no accident that the state has become a key testing ground for federal judges’ willingness to embrace same-sex marriage after last year’s strongly worded pro-gay rights ruling by the Supreme Court. Judges appointed by Democratic presidents have a 10-5 edge over Republicans on the Richmond-based 4th U.S. Circuit Court of Appeals, formerly among the nation’s most conservative appeals courts.

Nationally, three other federal appeals courts will soon take up the right of same-sex couples to marry, too, in Ohio, Colorado and California. The San Francisco-based 9th circuit is dominated by judges appointed by Democratic presidents. The Denver-based court, home of the 10th circuit, has shifted from a Republican advantage to an even split between the parties, while the 6th circuit, based in Cincinnati, remains relatively unchanged in favor of Republicans during Obama’s tenure.

U.S. District Judge Arenda Wright Allen’s ruling Thursday, that same-sex couples in Virginia have the same constitutional right to marry as heterosexuals, represented the strongest advance in the South for advocates of gay marriage. She put her own ruling on hold while it is being appealed.

Jon Davidson of the gay rights group Lambda Legal said the “very dramatic” shift in the 4th circuit was an important reason for the decision to sue for marriage rights in Virginia, which also twice voted for Obama.

Judges’ party affiliation is not a perfect predictor of outcomes. Republican-appointed judges in California and Kentucky have written opinions in favor of same-sex marriage. An Obama-appointed judge on the 10th circuit provided the decisive vote in a family-owned company’s religious objection to covering contraception under the health care law. And most notably, Chief Justice John Roberts, a GOP appointee, joined with the court’s Democrats to uphold the health care law.

Still, just over 60 percent of appellate judges were Republican appointees when Obama took office in January 2009, according to Brookings Institution scholar Russell Wheeler. Just over five years later, Democratic appointees hold more than half the seats on appeals courts.