As pointed out above in this series of comments, the producers changed Bonds AND rebooted and yet kept the same actor to portray M who had started with the then-new prior Bond actor, too, back in GE. And, clearly, the CR re-boot indicated a new background and history to the relationship between Bond and M, even though the M actor was the same. So, she started as a new M, with a new Bond, twice ! And I don't think it threw ANYONE for a loop.
Ralph Fiennes is so very fine an actor, as well, that he could do the same. Which is to say -- portray M with a new Bond, starting a new history. He could even play M in a period Bond after portraying him twice in contemporary Bond films. if the producers wanted to go back to the 50s/early 60s with the next Bond actor. (I've discussed this elsewhere. It would work well with a Bond actor who, either by their own age or preference, would play Bond for just, say, a trio of films. Also -- the period approach might be quite welcome, but be well done and ready to move on after about that many films.) If they made the Young Bonds into a series, he could play a character, recurring or not, in that !
This is nothing new for the films. They've had actors play different characters before. A wrestler in FRWL becomes a fellow British agent in TB. British Intelligence's Henderson in YOLT becomes the VILLAIN ( !!!! ) just 4 years later, 2 films later, one return of first actor later such that they made 2 Bonds together in a row between themselves, in DAF. And -- it was all quite OK with the audiences. (Poor Mr. Henderson, had he just taken a well-timed jump to the right or step to the left, he might have danced his way to safety !)
And it is not unique to Bond. Sergio Leone and Clint Eastwood made just 3 Man with No Name films together, and the same terrific actor (Gian Maria Volonte) played two entirely different lead villains in two of the films ! The first two of the trio -- two films in a row ! Confusing ? Considering the similarities of the characters, their behavior, appearance, etc., yes. But those films still were well received and are revered to this day.
You know what ? Get the best people you can and make a great film. That works. If this means Ralph Fiennes follows Dame Judi Dench's lead in playing the same character to two different Bonds, with two different histories, fine by me and -- as the examples above indicate -- would be fine by many others, too.