I'm not a Christian and I do see it that way. I believe just by rewriting the state constitution to include same-sex infringes on religious beliefs.
You keep saying this but you don't explain it. HOW does it infringe? What is it forcing religious groups to do that they are opposed to? This has zero affect on the ability of religious groups to live their life the way they want. Unless you can convince us otherwise I don't see what you're getting at.
And lets look at this concept of legalizing something that some people believe to be a sin.
I know of groups that find using caffeine, smoking, and drinking alcohol to be a sin. But they are legal actions. Have we infringed on that group's religious beliefs? Should we outlaw coffee, sodas, cigarettes, and liquor? No. Why? Because allowing these activities does not force those groups who find them wrong to actually do them.
Some very conservative groups find the use of electricity and industrial technology to be a sin. Have we been infringing on the religious beliefs of the Amish for well over 100 years now? Should we outlaw the use of new technology? No. Why? Because no one is forcing the Amish communities to wire up their houses.
The first commandment says "Thou shalt have no other gods before me." Which means that to Judeo-Christian groups worshiping any other deity is a sin. Should we outlaw all religions that don't worship the god of Abraham (Pretty much anyone outside of Islam, Judaism, and Christianity)? No. Why? Because if my neighbor chooses to worship his dog as a god it does not mean that I can't worship whatever god I want to worship.
Legalizing gay marriage does not affect religious groups in any other way than to make them feel insulted that they must use the same legal term as a gay couple. And as far as I know there is no right to not be offended. Christians who attempt to prevent gay people from being married are doing the exact same thing as an atheist who tries to prevent them from displaying a nativity scene in their yard because it offends him.