Orthodox clergy generally feel they are precluded by traditional Jewish law from officiating for these couples. Their stance is supported by the law; they cannot be forced to perform ceremonies they feel are not in compliance with Jewish law and tradition. That said, some Modern Orthodox clergy may be approachable for private blessings, if not a public ceremony.
An LGBTQ+ couple needs to make an essential decision as they approach the design of their ceremony. Are they looking for a ceremony that models a traditional ceremony, or one that is decidedly different from it? One couple might downplay that their story of “love is love” is shared by two men. Another couple might wish to lean into a “queered” ceremony, as a better reflection of their own identities.
All of the non-orthodox rabbinical organizations offer at least one option along each of these models in prepared rabbinical guides. A willing rabbi or cantor can provide those options to an interested couple. These ceremonies are crafted with deep sensitivity to the couples who seek them out. Keep in mind that denominational commitments will inform a ceremony’s structure, content, and language. Independent rabbis and cantors are generally far more willing to work beyond any restrictions denominational clergy might have.
There are many resources available beyond any particular denomination for the DIY or deep-dive types. Run a quick search and you will find that there are different terms that refer to the nature of the ceremony for those who find the traditional wedding terminology inauthentic.