I think it depends on how long you plan to keep the sofa and how long you plan to keep the chairs. I find the extreme color contrast combined with the texture contrast too jarring for my taste, so I wouldn't want that mix long-term. If both pieces are long-term investments, I'd look for a fabric for the chairs that has more of a dark and light mix, to make it look like a more purposeful transition. If the chairs are long-term and the sofa is just a placeholder until you can get what you really want for the new house then make the chairs exactly what you want with the idea that a better sofa that ties in is on the horizon.

I mixed leathers in our living(not my first choice but that what I've got at the moment), but brought also lots of other fabrics in different textrures. Velvet, linen, embroidery, cashmere, felt, knit... Also have lots of other materials there-the coffee table is glass, the side table is seagrass woven stool...have ceramics, brass, plants of course.. can be pulled off if you don't leave it just one tone thing to me gray and brown can be interesting..depending on what shade is gray and what is brown. Not sure though I'd combine them in leather.

ETA: Disregard these suggestions, which were based on your original written description only, since you hadn’t yet included a photo. I was visualizing a formal living room in a classic colonial-style home.

Congratulations! Beautiful home. You absolutely can mix them, it can be a wonderful look. When I was a kid, that type of traditional paneling was very popular (late 70’s) ... and lots of people had MCM and modern with it. We had it in our living room. It’s always been a thing in old European homes, too. Just wanted to show a few pictures of mixing Mod with ultra-traditional — I’d just look around at other examples, and start hunting for the pieces you want to add in there. And you can certainly mix the furniture and accessories styles, too. For me, it’s helpful to put things I like together on a mood board (online) and get a feel for how things play together.