Outside of religious conservatism, the issue of equal rights for lgbt people, including to marry the person they love, is mostly settled in developed parts of the world, with some exceptions such as in Asia.
In the U.S. alone, the American Medical Association, American Psychiatric Association, American Psychological Association, the American Academy of Pediatrics, among others, all support marriage equality for lgbt people. So do similar professional bodies in many other developed countries. The relevant professional organizations do not consider gay conversion therapy to be an effective treatment, some going so far as to say that it is very harmful, and it is banned in some areas, because sexual orientation is largely outside of the realm of choice.
The rate of lgbt acceptance and rights worldwide is mostly correlated with education, with the more educated countries mostly being in favor and the least educated countries being mostly against.
The reason gay marriage is compared to interracial marriage is because it's essentially the same: People who have nothing to do with that particular marriage want to come in and block two consenting adults from getting married despite not having anything resembling an evidenced argument as to why their opinion on the subject should matter.