It takes Luke 3 years of training between 4 and 5 to be able to move his lightsaber in the Yeti cave. But some stupid kid can move a broom with no training? And you think that’s good writing?
Star Wars has years of back story and “rules”. You don’t just become a Jedi by accident, it takes years of focused training. The Last Jedi craps all over that. It says anyone can do what Jedi do without putting in the effort. It takes the Star Wars mythology and throws it out the window. And you think that’s good writing?
I think this is very fair criticism. Canon does put 3 years between ANH and ESB, a period where the Marvel comics take place. Luke does do a lot of independent study during this time. BUT... canon does go back and forth on "accidental magic". Luke has to be coached into feeling the Force by Obi-won, which is the reason he can then feel it in the X-wing at the end of ANH. He does struggle with training in ESB and gets cut to pieces by Vader. When you compare that to Rey it is aggravating. However, in the prequels, Annakin is not coached into feeling the Force BUT Qui-gon implies that the only way he is competitive in the pod race is because he is using it instinctively. So there is room for accidental magic, but it's not real strong on using the physical side of the Force, more on early stage "let it guide you" type of stuff. There is also, I think, either six months or a year between ESB and RotJ, so again, Luke can incorporate his training with self study for a period of time. Since the total timeline of TFA and TLJ is probably less than a month, you just can't say the same about Rey.
So the kid with the broom isn't total anathema, it's just Johnson wanting to beat a topic into our heads that has limited support. I don't think the point is "anyone can use the Force." I'll be surprised if they go this way. I think they are just pointing out you don't have to be a Skywalker or related to a Jedi family to have the Force. This is 100% canon, as Jedi were forbidden attachments and didn't have kids (I think the Ruusan Reformation was mentioned in Clone Wars, making it canon, but regardless canon is quite clear on Annakin and Padme). Over thousands of years they would have bred the Force out of existence if it didn't spontaneously manifest on a regular basis in new kids. Plus they wouldn't have to go looking for Force sensitive kids, they could just track families. So I have no problem whatsoever with random kids developing a connection, I would have a huge problem if all kids developed a connection.
I do think there is room for a lot of complaints about TLJ. In my opinion Johnson took too many liberties with canon. But again, Star Wars has never been the most orthodox of canons because so many fingers have stirred the plot. Sure there are 2 trilogies with Lucas's fingerprints, but those total around 12 hours of story. There are over 30 hours of Clone Wars shows, around 20 hours of Rebels, many comic episodes, some novels... all canon without dipping into the now defunct EU. So there is wiggle room and fans need to accept that so many viewpoints have impacted the canon that a single orthodox interpretation is almost impossible.
Ruining Luke, however, is still unforgivable.