I've never heard anyone speaking or complaining about anyone else speaking Navajo on NA servers. Given that there's probably very few native speakers of Navajo that seems really unlikely. It's one of the few indigenous languages in the US that isn't totally dead but it still has very, very few people that speak it and I'd guess that all of them in the demographic age for Overwatch are fluent in English too.
Mostly what you see on NA servers is English, Spanish, and Portuguese. But since it tends to sort people by ping/region, most LA and BR players tend to get grouped together, so there are very few matches of mix languages. The only time I've ever ended up in a match with all Portuguese speakers, for example, is when I grouped with a friend living in Brasil (then I was the annoying person who didn't speak the same language as everyone else). Otherwise, I see one or two here and there in games but mostly the server grouping tends to prevent people from getting stuck in games where they can't understand each other.
Anecdotally, I'll bet most NA players get grouped with Asian players playing on US servers far, far, far more than Spanish or Portuguese players. That seems a lot more common.
Ultimately, outside of high level Comp, I really don't think it matters that much anyway. People whine far too much about the language issue in general. OW's emote system is fairly robust and the objectives simple enough that unless you're playing at a high level, you can do fine without advanced communication.