I think you should give it a go.
RDR1 shared many similarities with gta, but I felt connected with the story and its characters in a way that I had never been before with a gta game. I think GTA V improved on that point, but still, I think RDR1 story was far better. And as someone said, you may only follow the main story line and ignore all the side quests and the map exploring, however, I bet you’ll be missing on a lot of good stuff.
Btw, you should not feel embarrassed for not liking gta games. Although I really enjoy them, I think they have a lot of room to improve on the 'story telling’ department.
Whenever I tell somebody I don't like GTA games, I get conversations comparable with this: