Sorry, but my parents do not like or support gay marriage because of their religious beliefs. They are not bigots. They are not homophobic. They have their religious beliefs. They treat lgbt just like every other person. They believe marriage is sacred; a belief informed by religion. They are not bad people for having that belief.
First of all, what they do inside their own home is up to them. However, since they appear not even to comprehend the history of "marriage," I sincerely doubt they are completely tolerant of society's definitions and laws regarding marriage.
Next, if they subuscribe to a homophobic religion, then, yes, they **are** homophobic and they **are** bad people. If they do anything in any part of their life that is based on religious rules rather than on reality, then they are just plain wrong. Let me point out further that I don't give a rat's ass whether their religious leaders will allow a **religious** marriage to gays. Marriage is a legal status (just ask those of us married via legal documents and a J.P.), and neither your parents nor their religion has any right to comment on that.
Your fundamental failure here is that you are claiming that your parents only hold opinions when in fact they are trumpeting their positions as facts.