Does this essentially boil down to an objection to the use of the words "marriage" and "sex" to describe anything other than heterosexual marriage and PIV intercourse (because if so, I get that) or is there something deeper I'm missing here?

It's pretty much about definitions and the logic that flows from them. If you see sex as solely a procreative act, then what gay people do is not sex. If you see marriage as a partnership (or sacrament) between a man and a woman for the purposes of raising a family (almost always in the straightforward biological manner) then same-sex partnerships are not marriage. I can appreciate spiritual perspectives that would dictate such definitions (I don't necessarily want to go into them here in detail but they would be based on an archetypal realm of reality). Whether I agree with these definitions and perspectives is irrelevant, there are people in the world who do and their perspective matters. As does the perspective of people who disagree. The larger point is that we all have to get along with each other and so we should seek rules, agreements, and understandings that allow us to do so without infringing too much on others' rights.

So, for example, let me have my civil union, "marriage", or whatever, with my same-sex partner, with appropriate tax, power-of-attorney, and inheritance benefits (since they don't impact you at all), and in return I will refrain from insisting that the partnership is a "marriage" by the standards of your religion, and I will respect your desire not to be involved in the ceremonies, celebrations, etc. TRAs don't do that: they're in everybody's face, all the time, with no respect for the feelings of others.