I would almost always use "my partner" after getting serious about a relationship (and I use it about my girlfriend).
I'm not particularly political about it myself, because I don't have to be, but in a country that has only just legalised same sex marriages including those between trans people who may have a complicated legal status, the political content of retaining the words "wife" and "husband" together with the associated historical cis-and-hetero-normative assumptions and values is fairly obvious.
The question of how best to address that content is a bit less obvious. I know quite a few LGBT people and they would have different views on the subject.