Well, for one, there's the belief that homosexuality is a tendency caused by social decay and creates hedonistic and individualistic people. This comes from more then one source, with the most famous comming from communist regimes, who believed homosexuality was the result of a capitalistic society and a product of the bourgeisie (I hope I spelled that right :v). This comes mostly from Engels rather then Marx, which isn't surprising since Marx was both financialy and intelectualy dependent on Engels. Alas, dirty commies.
Another common one (mostly used by atheists who do not support homosexuality) is that homosexual couples do not contribute to the evolution of humanity because of being unable to breed, and in fact only contribute to the elimination of their own genetic traits from the DNA pool. Some argue that this isn't a critical issue since science can correct this problem, though.
Another one is that homosexual parents are unable to provide the same environment that a heterosexual couple provides to children, and thus a homosexual couple's child would have developmental problems. Some say that the lack of proper male and female role models in parents is the main cause of gender dysphoria, but thats a really shady argument IMO.
A more "slippery slope" one is that homosexual men and women are more likely to be involved in substance abuse, which is actualy supported by some statistics, but one could argue that this is mostly caused by society's hatred of gay people, rather then something that comes with homosexuality.
Anyway, I'm making clear here that I do not support any of these opinions/views, I'm just pointing out that they exist and are independent from religion, altough they can often intersect with it.