No I don't "get you,".
If someone tells you they identify as non-binary and they preferred to be referred to as "they/them" then I would use those pronouns out of respect.
If someone is non-binary and says they have a preference for "he/him," although they'd accept "she/her, they/them," I would call them he/him regardless of how they present. For example Jonathan Van Ness is non-binary and prefers he/him regardless of how he presents, and out of respect he should be identified as such.
If you, or anyone else, has an issue with using the correct pronoun for someone because "you don't see them as that," based on a societal construct of what masculine and feminine look like, then that is very much a you issue. They aren't demanding that anyone view them as such but that they are referred to in the proper way. That's just basic respect for other's.
It is in no way similar to someone "marrying a train or identifying as a cat," which is the example many people give and only shows their ignorance.
People are demonstrating their blatant disregard for the lgbtq+ community in doing what you have.