Respecting someone's beliefs should be a given. I'm not particularly offended that someone chooses to believe something that cannot by definition be proven either true or false, although it does seem very alient to me.
However, religiously motivated intellectual dishonesty is a different thing altogether. That is what most religious factions (christian or otherwise) do with their position on the rights of sexual minorities. Specifically the dishonest argument is that marriage originates from religion and thus religion (and usually one particular religion) should have the right to determine what marriage should be and who's qualified to marry.
Of course this is false - humans pair-bond with or without religion. In the societies of olden days, churches were not just religious institutions but also fulfilled the role of magistrates and census was regularly done based on parish upkeep. They also kept note on who were the parents of a child, etc. With such important functions in historical context, of course churches also officiated marriages in most cultures. It's just that the three Abrahamic religions tend to be so obsessed with sexuality that they all pretty much decreed that you should only have sex after given permission by the church - ie. after being married (although this is not exclusive to Judaism, Christianity and Islam - it seems to be a common trend with patriarchal societies in general).
In the modern society, no one needs to ask the church's permission to have sex. Instead, marriage tends to have more of a legal function, and refusing that from certain types of couples is against the principles of equality. And before someone brings up the slippery slope argument again; no, granting marriage right to same-sex couples doesn't mean you should allow any kind of relationships to be registered as marriage. Just all relationships between two consenting adults.
Another good examples of religiously motivated intellectual dishonesty would be creationism, "intelligent design" and abstinence-only sex education. Since these often are advocated by very religious christians, it can often seem like "christians are not tolerated", and since this suits the propaganda purposes of the ultrareligious organizations, they like to repeat it as often and as loudly as possible, and if you object you're not only satan's servant but also an oppressive person persecuting people who just want to practice their religion...
I would have the same contempt toward anyone who wished to bring complete, falsified nonsense to public education as part of official curriculum, regardless of their reasons for it.
What would your reaction be if schools started teaching that maybe NASA didn't send people to Moon after all, just because some uneducated people don't understand how it's possible and present some arguments based on incorrect premises that "prove" that it's either impossible to go to Moon, or even if it were possible, the pictures are still fake...
Or how about teaching Aristotles' Theory of Impetus as an "alternative" to Newton's mechanics?
Because these are exactly on the same category as teaching creationism or intelligent design as "alternatives" to evolution as the source of diversity of life, or cosmology as the origins and structure of universe.