Hypothetical: Funeral home hires a man. He works there for 6 years, and does well. Then, in the 7th year, he starts wearing women's clothing and make-up, and insists that people call him by a female name and use female pronouns. This creates a stir amongst the elderly attending funerals and detracts from the solemness of the wakes and funerals. Soon, the word gets out, and everyone is going to the next town over for wakes and funerals. So, the funeral home fires him.
Did they fire him because of his sex? Obviously not. He is a biological male, and he never transitioned physically, so he is still a biological male. They hired him as a biological male. They would continue employing him as one.
Did they fire him because he was driving away customers? Yes.
The only issue should be: Is the reason he was was fired not based on a protected class (e.g., because he was driving away customers)?...Or, is the reason he was fired because he was in a protected class (e.g., an African-American, or a woman). If the latter, that is illegal. If the former, that is fair game.
The issue would be the same if he started getting curse words tattooed on his face. Tattoo wearing is not a protected class (or it shouldn't be). Same with sartorial choice--not a protected class (or it shouldn't be). Employers should be able to fire for both. The Court seems to have made one a protected class.
If I get the time later, I will read the case. I'm just going on what the article said, and the first page or so of the case.