I don’t think those genres are mutually exclusive. I haven’t played RDR1 but RDR2 is definitely an Action-Adventure RPG. You level up Arthur’s stats throughout the game and can choose different moral paths that affect the ending. That’s playing a role.
Likewise, I haven’t played RDR2 (started, but never got past the first 30 min or so), but RDR1 is pretty much just GTA in the wild west. You can buy stuff (like GTA), but I don’t recall any stats to speak of, it’s very much an action-adventure. Wikipedia claims RDR2 is an action-adventure, so I assume it’s closer to the Yakuza series in terms of character customization than RPGs, and Yakuza games are very much action-adventure (despite having some skills to level up).
I mean, define ‘RPG’ because to me, any time you choose how your character evolves and grows as the game progresses through a story, that’s an RPG.
There isn’t really a single, clear definition of “RPG” because it’s a really big genre, and a lot of games have taken mechanics that used to define RPGs. What defines it for me is whether the development of the character (in terms of stats, equipment, etc) is central to the gameplay.
For example, Elder Scrolls games are absolutely RPGs. You customize a character, assign stats, collect equipment, and game interactions are largely based on stats. The whole focus of the game is on that character development. JRPGs push the limits of an RPG somewhat because there’s a lot less player interaction with the stat systems (i.e. number just goes up), but the gameplay is highly dependent on those stats. As you stray further, we get into ARPGs, which frequently focus more on the action than the role-playing aspects, but the role-playing aspects are still very central to the game (e.g. Diablo, Ys, etc).
RDR, on the other hand, doesn’t really rely on stats for gameplay. You can completely ignore the stats and enjoy the game. There also aren’t really any meaningful choices when it comes to how the player develops the character. Yeah, I guess if you do bad stuff you’ll get a bounty or whatever, but that’s not what I’m talking about, I’m talking about gating off parts of the games because you chose to pursue one stat over another.
A lot of games borrow elements from RPGs (e.g. looting, skill progression, etc), so there’s no clear definition that clearly delineates which ones are or are not part of a given genre. Genre labels are supposed to be informative about what to expect in a game, and me describing RDR as an action-adventure game is a lot more informative than calling it an RPG.