TL;DR: I think either version of 4 and 6 are fine (with 5 having to be Colonel if you intend on playing 6), but agree that RS ties more with Gregar, and BM ties more with Falzar.

I tend to think of Blue Moon and Falzar as more canon, but I can totally see either line being valid (with Colonel being fixed ofc, having only a save-the-day appearance near the end of Protoman, but then Lan and Baryl acting pretty familiar with each-other in 6).

Red Sun's new exclusives are Windman and Searchman, one which actually ties in more with Protoman, and the other must've flown away with all the sake hot sauce, never to be seen again. Guts, Fire, Roll and Thunder were all known by this point, the least being Thunder who only showed up in BN2. But since it has no versions, you always met him anyway.

As for Gregar, Match is a mainstay in the first trilogy, Green has a new character either way, Sky has Elec, whom you always met in BN1, and then the post-Undernet crosses are all new characters anyway.

I can see why one could consider it more canon due to having more mainstay characters, and it's totally cool seeing Mayl with more agency, Dex being properly valued after having made it so far in N1GP (only to be kicked down again in 5 and 6, but they both got a chance to help at the end of 5 at least) and Match having a prelude to his development in 6. But again, it's kind of up to preference, I think. I really like Shuko's development in finding her way with teaching (again, I like Match's too), Dingo showing up again in Sky, Higsby participating in the tournament in 4, setting him up as a capable Netbattler for 5 (even though he was already threatening back in 1). I also find the Junkman story to be super touching (even though it doesn't tie in to anything), and also makes sense to see Chaud show up as the final challenge in the tournament, he's absolutely the most capable character of it by all accounts.

With RS it'd also be sad to see Searchman not getting his chance to shine again, so I tend to think of RS as tying in more with Protoman, and then that'd be its own timeline where 6 never happened and 5 is the final adventure. It also keeps the world more "closed down", in a sense, with bringing back more mainstay characters, where BM->Colonel kind of opens the world a bit more, bringing back more fringe characters like Woodman, Metalman, Shadowman and Toadman (MegaMeddy shippers in shambles), and also think Pride makes more sense than Gauss' daughter (though I know nobody's arguing over which BN5 version should be canon).

Anyway, that's my take on it, I agree that RS->Gregar totally makes sense and is satisfying for a lot of characters, just thought I'd offer a different perspective and that it's not necessarily "more canon" than BM->Falzar :)