Again, how do these things change the story being told? Is Kirstie Ally's face an important part of TWOK? Is Kyle's ethnic background important to any of the TOS episodes he's in? OTOH, the 78 decks do figure in the story of TFF, but they don't actually change the story being told. (Which can be told with almost any number of decks)
Transporters destroy and recreate matter, so none of the characters are ever the same from one episode to the next. They really should rename her the USS Theseus.
Kyle can be explained very easily: Chapel is there to pilot test the genetic manipulation they use to blend in. In the last episode, I bet they'll have a reason for Kyle to join in a mission that requires him to look like a northern European male with blonde hair and a British accent BUT the change never wears off - and as a result Star Fleet CANCELS Chapel's project and sends her back to the Civilian research facility... Simple.
Are both Robert April’s different characters? I don’t think anyone has a problem with more diverse characters since 340 years in the future there is unlikely to be any white humans left as they will have been deliberately bred out. Although that would also mean no sophisticated starships as there would be no white men around to invent and build them, so no starfleet...
You're making a very weak comparison. The other primary characters are well-established as their TOS counterparts by backstory, dialog, full names, etc. An engineer working on the Enterprise many years before TOS with a single (first or last?) matching name could very well be a wink at Trek super-fans, particularly given that he was an extremely minor character. There isn't anything else presented to tell us this is in fact meant to be that character. (Though given the ridiculous reaction some people are having, I really hope that it is.) For the sake of us all, I really, really hope that's supposed to be a joke.
Transporter chiefs surnamed Kyle, yeomen surnamed Colt, and navigators surnamed Mitchell are a dime a dozen - starship captains named Robert April are rare.
Looks like the same guy to me! Answering your question earnestly: I don't consider anything from TAS to be binding for continuity except broad details, and sometimes not then. The Bonaventure 10281NCC from "The Time Trap," for instance, is just completely incompatible with the rest of ST canon. This is the same cartoon in which people, inanimate objects, and animals were routinely painted with the wrong color. I have no problem accepting the broad outlines of Robert April's life from "The Counter-Clock Incident" while disregarding his depiction as a white guy. In my headcanon he's still married to Sarah, for instance. Ah, there is. The unvarnished white supremacy. Figured it would come out eventually. Though I see you're already banned!
I could not possibly care less whether's he's Irish, Asian or an intelligent giraffe. Do people really sit around worrying about this shit? Gee whiz Guess what, the ship doesn't look the same either. Who fucking cares?
Voiceover: "Today, due to illness, the character of Brooke Logan-Forrester will be played by..." ["The Bold & The Beautiful".]
No matter who plays him, Kyle must be a real loser to be a lieutenant on Pike's Enterprise and then still a lieutenant on Kirk's Enterprise a decade later. A 23rd Century Harry Kim!