This in no way changes the fact that religions do not own marriage, so it is not adopting a religion nor infringing on any religion's rights for the government to allow same sex couples to marry. <---This was your contention. Bringing up what the government originally had as marriage does not change the counter to this contention.
"A woman is like a teabag, you never know how strong she is until she gets in hot water." - Eleanor Roosevelt
Keep your religion out of other people's marriages.