I said "It would be the same" not because I actually believe that but because I think that, on balance, religion's influence is exaggerated and where religion has effects they tend to be a pretty even mix of positive and negative.
It's very easy to look at the people yelling homophobic ideas, misogynistic beliefs, out-dated and closed-minded concepts, ignorance, and bigotry as a result of religion. But there are millions of practitioners who quietly work. There are thousands of services churches provide. Just today, I was reading about how religion helps women cope with intimate partner violence. The Catholic Church is a vital source of assistance for these women. Moreover, many of the most impressive social movements have had a strong religious membership, from the civil rights movement in America to the solidarity movements that helped carve out a little safety from dictators and death squads in Latin America in the 1980s.
Religion's causes of negative behavior are overwhelmingly through the institutions and biases we already have. I think that people are homophobic because of culture and they sublimate the idea through religion. From the Crusades to today, what has looked like clashes between religions or civilizations has almost always been straight power politics in disguise. The Crusades did far more damage to the Byzantines than they did to the Muslims. And as much as Samuel Huntington might protest otherwise, America has often opposed Christian governments and peoples while backing Muslims.
I don't too quickly want to dismiss the idea that religion can itself be an institution that contributes to harm. These factors are cyclical: Homophobia may not have had the pedigree it did if religion didn't sublimate it and protect it. But I truly believe that, if we dealt with our moral paucity and our unjust institutions as a species, religion would be benign.