Apparently, marriage is allowed in Elder Scrolls: Skyrim.
For example, as a Human, if I wanted to show my love for an Argonian or Khajit, and they were up for it, would I be shunned or treated differently by NPCs?
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Skyrim's idea of romance is pretty tame compared to other RPG franchises (like Dragon Age and Mass Effect from BioWare). For the most part, who you marry is completely irrelevant, and nobody will comment about it: Skyrim is a very forward-thinking kind of place.
The official guide confirms this, even highlighting the lack of racial effects on marriage as a bonus.
So go and marry that Argonian, we won't judge (not that there's anything wrong with it).