A marriage is for two people. There is no sharing of marriage between people. There is no zero sum game where same-sex marriages change the nature of opposite sex marriage.
And, legally, you can create a large bathroom that caters to both sexes, if you would like. Besides, there's no deprivation if someone who is comfortable using such all gender bathroom uses a sex-segregated bathroom.
So, this is just a stupid argument.
There are those opposed to SSM who would dispute that, tho certainly that is what civil marriage is primarily about these days. I would agree with you that same-sex marriage does not change the nature of opposite sex marriage.
However, the bathroom analogy isn't a good one as we don't have a situation where everyone isn't provided access to a bathroom for their gender. (Unless you're going to argue we have more than two genders by using a definition not based on physical attributes.)