As I see it, the issue with a RDR3 set chronologically after RDR1 is that you get pretty close to using cars; and you can't be "GTA with horses" if you have cars :P
But you could still squeeze a game there and still limit or not have cars at all. Would further the "transitioning from the Wild West to the Modern World" theme, but I think being able to use cars is the line of demarcation between the two series.
Plus you are getting closer to WWI. RDR1 takes place in 1911, WWI is 1914-1918, so you can set it around there. After that you get into Prohibition territory which is definitely more GTA than RDR.
Going backwards is where there is more runway, but always being mindful that the further back you go the closer you get to the Civil War.

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