This seems to be too obvious to need confirmation. Nonetheless, it is nice to be data. What is the most common reason people who oppose marriage equality for gays give for their opposition?
Mind you, the 47% is the tip of the iceberg. Not infrequently, those who get their homophobia from religion lie about their true motives, such that it wins support from more people. (To be fair, some of those who support same sex marriage also name God/religion as the reason, but only 5%).
And here is more evidence of religion causing homophobia: guess how support with marriage equality is related to church attendance, and to age groups and political affiliation.
These findings are corroborated by another recent study, on regional distribution of support for equality. Not surprisingly, that is far from homogenous.
And hence, regionally, support for equality seems match religiosity inversely, rather neatly:
Lastly, check this out to see why religion literally causes backwardness: when it comes to equality for gays, the most religious part of the country trails the rest of the nation by 10 years.
It really should not come as a surprise that atheists and agnostics are the most progressive on this issue, with 90% support for equal rights for gays.