Well I could be the poster child for the phrase "soul sucking beige"; warm tones general are bad on me, and beige is the worst. And yet, my trench coat is beige, and I wear it all the time. I actually gave away a black one because I never wore it (made me feel like a stormtrooper).
I'm sure it helps a lot that it's a cool tone, really a light shade of taupe. And I always have an intervening layer of a more flattering colour at the neckline whenever I wear mid-tones, because i need contrast. If I don't have a collar or highish neckline, usually in white, black,
or navy, I will add a scarf or bandanna.
Even before I found the right-for-me shade of taupe, though, I was able to make it work. I realized this when I was given a trench style coat in a warm beige -- that had a removable lining in bright red, that also framed the collar. That changed everything. When I realized that the bright at the neck let me get away with it, I found myself a scarf that combined black, white, red, and beige-taupe, and wore it with the coat in terms seasons too warm for the lining.
So: by all means, enjoy a coat in pink or teal or navy or whatever colour brings you delight. But if, like me, your little preppy-classic heart beats for a traditional trench coat in traditional beige: yes, it can be done.