For me it really depends
My favorite alternate history books are not even remotely in the realm of possibility but I still like a serious work every once in a while
Let’s hear the community’s thoughts
In general, I care more about quality writing and an entertaining story than I do about the plausibility of the story’s point of departure.
I enjoyed Turtledove’s Worldwar series, despite the implausibility of not just an alien invasion, but an invasion by aliens who were culturally resistant to change.
I like alt-history where it looks like effort was put in to tell the story in a way that makes sense.
Not all historical events were “realistic”, so expecting all alt-hist to be would be unfair, but the reason for the deviation from sense needs to be well justified in the text and world building for it to read like anything other than “X-aboo makes everything go right for X” power fantasy fiction.