Q: Please explain what this passage means from Obergefell v. Hodges (U.S. 2015), and how are the beliefs of people opposing same-sex marriage not disparaged by this decision (bolded part)?

"The right to marry is fundamental as a matter of history and tradition, but rights come not from ancient sources of the Court alone. They rise, too, from a better informed understanding of how constitutional imperatives define a liberty that remains urgent in our own era. Many who deem same-sex marriage to be wrong reach that conclusion based on decent and honorable religious or philosophical premises, and neither they nor their beliefs are disparaged here. But when that sincere, personal opposition becomes enacted law and public policy, the necessary consequence is to put the imprimatur of the State itself on an exclusion that soon demeans or stigmatizes those whose own liberty is then denied. Under the Constitution, same-sex couples seek in marriage the same legal treatment as opposite-sex couples, and it would disparage their choices and diminish their personhood to deny them this right.