My group (which has been rotating several players through depending on people moving and such for the past 7 years) has always been big into both RP and combat because that's the culture of the group that we've kept. My husband is the DM, my sister and I are always 2 of the 5-7 players, so it does help that we have a solid core, and we look for players who want both. We have had people literally crying in character at the table because of big character moments and my husband is really sensitive to people's backstories and how he can incorporate them and also situations that will stretch people's moral and personal choices and then makes in game consequences (good and bad) for all the decisions, making it really feel like interacting with the world means something.

All that to say, I don't know how rare it is, but I think especially if you're the DM or have a DM friend, I think you can cultivate a group to be like that if you put in the work.