Ah. You've never been there. El Moro is not a bar scene of any sort; it is a small-ish family run restaurant back in a residential part of town. It's true that there are many great restaurants on Cozumel; El Moro is right up there amongst them. If you skip it it's your loss.
I have been there many, many times, and the only time I remember encountering a big noisy group there I was at that table. It was for my mom's 90th birthday party. Ray and the rest of the family went all out to help us celebrate; the old man even came out and danced with my mom to Marvin Gaye's Let's Get It On.
There were other customers in the place, and they all joined in with the singing of Happy Birthday and the cheering thereafter. Several total strangers came over and paid their respects to my mom. No one appeared to be inconvenienced.
So, anyway, my advice is to cab it to El Moro on an evening other than a Thursday (they are closed on Thursdays) and have the cab wait while you take a look at the scene. If it is not to your liking get back in the cab and have it take you somewhere else. Chances are it will be fine, and if you eat there you will not regret it.