I know Córdoba a lot less than Buenos Aires (where I'm living at the moment, by the way).
But I've heard only good things, from Argentine friends, about Córdoba, a big right wing city with an independent mind and vibe, and even its peculiar accent. Plus, it's not really aligned with the current government (note that Mendoza is even more opposed to the central government, to the point of occasionally talking about secession).
Well, Argentina like all non-Muslim, non Russian, non Sub-saharian countries, has a small, troublesome, crazy minority of LGBTs who do noisy, ugly stuff in the media and sometimes on the streets.
That's the world we live in. Even Hungary, for example, has (from what I've read) a crazy gay-friendly city boss in Budapest, actively trying to undermine Orban and the Conservatives.
It shows that, only Muslim States, Black States, and Russia/Belarus, are free from public LGBT decadency.
But anyway, consider this: in Argentina and a few other South Am countries, sure you have a few LGBTs, but you don't have 'crazy' Talibans, hungry Africans, or 7 months of Siberian cold. One has to make choices. Nothing is perfect. Russia would be perfect with 8 months of Summer and a simplified language, but, it is what it is, and under current circumstances, Argentina or Chile are quite very good (and non expensive) choices to live in.