I never thought that "marriage equality" was considered morally loaded.

I know enough social conservatives who oppose(d) same-sex marriage to say that at least a large minority considers it to be morally loaded, and I think it is as well. Opponents of same-sex marriage, just like liberals, think that equality before the law is a moral imperative, but they have a different idea of what constitutes equal treatment. On an abstract level, opponents of same-sex marriage oppose it because they don't see it as equivalent to heterosexual marriage in some way or another. Consequently, to acknowledge that same-sex marriage is equal to heterosexual marriage is to give the game away.

Of course, that makes it a useful rhetorical strategy for liberals to frame the debate in terms of equality--and I suspect that's precisely why some liberals advocate for the term.