From VOX

Does all of this apply to interracial marriage as well?

The legislation states that the same protections it provides for same-sex marriage apply to interracial marriage as well.

The right to interracial marriage was established by the Loving v. Virginia case in 1967, which overrode state-level bans on interracial marriage, and is another precedent that some civil rights advocates worry could be threatened by the Supreme Court following the Dobbs decision.

Were this precedent rolled back, the Respect for Marriage Act would require states and the federal government to recognize interracial marriages, and give those in such unions the same rights and benefits as those in same-sex marriages. As with same-sex marriages, the law would not require states to issue licenses for interracial marriages if they decide to restrict it.