I just moved to Canada, where “This is my partner” seems to be used more than “This is my wife/husband”, even by straight people.
I find that *much *more jarring.
My brother has been dating the same woman for more than a decade, and living with her for several years. They are both divorced from their first partners (and the parents of their children) and they don’t plan to marry.
I refer to her as “my brother’s partner”.
A couple of decades ago, I attended the ‘gay wedding’ of a friend at a local Unitarian church. It was published, without comment, in the Wedding Announcements section of the local newspaper. This turned out to be something historic, the first gay wedding announcement to be published in a major city newspaper in the USA. Afterward, the local GLBTQetc. community lauded this uneventful publication as a great advance. Then the local fundamentalist religious responded, attacking it as a sign of the moral decay of the nation. Bit of a local tempest for a while.
Later my friend told me he had sent the announcement in as a bit of a joke. His fiancee had bought one of those How To Plan Your Wedding books, and was being a real groomzilla, obsessively following every checklist in the book. So he mailed off a wedding announcement to the newspaper, fully expecting it to be ignored. And was quite surprised when it was published.
And then another friend, who worked at the newspaper, told me the newsroom gossip was that this was a slipup – nobody noticed that this was a wedding of 2 guys, and they just tossed it in the column with the other announcements. (She thought this was quite possible – that section of the newspaper was staffed by the newest-hired employees, or the oldest ones serving out their last months before retirement.)
But then the Newspaper Management stood by this publication – because they refused to publicly admit to a mistake! They said their policy was to publish wedding announcements equally, without regard to gender. (But nobody at the paper had ever seen this ‘policy’ before that.)
Thus is History made.
Doesn’t bother me a bit.
On the other hand, it is gendered language. I have a slight preference for everyone to just use “spouse”.
I dunno if I’m comfortable about it - I’ve never heard it! (I live in Idaho, which is a land of barbarians. Plus my social circle can be counted on one hand.) That said, whether I turn out to be comfortable or not, I’ll certainly support them using the term. It’s correct, after all!
I guessed where your story was going as soon as I read the part I copied – and I bet that’s how a lot of history is made. 
I don’t object to it. I will say it disorients the “born in another time” part of my brain. But I am totally comfortable with married people saying they’re married.
One benefit of gay marriage is that the word “partner” is available for this sort of relationship.