While The Big Bang Theory's version of Meemaw was nothing like this, there might be an in-universe reason for this. Although Young Sheldon wasted Sheldon's best backstory, the same episode of the spinoff could have set up Meemaw's character shift. At the end of Young Sheldon season 6, episode 15, "Teen Angst and a Smart-Boy Walk of Shame," Missy runs away from home in her most substantial act of teenage rebellion yet. The fallout from this incident might explain the change in demeanor between Meemaw's Young Sheldon incarnation and the character's later iteration seen in The Big Bang Theory.
Young Sheldon's Meemaw couldn't remain a feckless, rebellious presence in the lives of her grandchildren forever without being seen as a bad influence on them. As such, it would make sense if Missy's decision to leave home was the catalyst that made Meemaw realize this. After all, throughout Young Sheldon season 6, Missy has been employed in Meemaw's video store that doubles as an illegal gambling room. While this plot allowed Meemaw to address Young Sheldon's main villain directly when the church attempted to shut her down, it still meant that Missy had a major presence in her life who got away with seriously risky illegal choices.
It doesn't make sense for the conservative Meemaw seen in The Big Bang Theory to be the same character as her Young Sheldon self unless there is an underlying reason for her attitude adjustment. Meemaw always needed to change at some point or another and, since Sheldon was never likely to become a rebellious teen, it makes sense that Missy leaving home could be the incident that steeled her grandmother's outlook on life. Meemaw might be open to taking a lot of risks herself, but she has repeatedly proven to be fiercely protective of her grandchildren which means Missy's acting out could worry her.
Much like Sheldon's grant database storylines set up many of The Big Bang Theory character's unusual character traits (like his obsession with credit), Missy's plot line could change her grandmother's viewpoint. Where Meemaw used to be a necessary corrective to Mary's worrisome perspective, she could become more like her daughter as she sees begins to fret about Missy going missing. The fact that Missy already snuck out to attend a frat party only a few episodes earlier proves that she is firmly into a rebellious teenage era, and it would be tough for Meemaw to warn her against this behavior when she is engaging in even riskier illegal antics.
By Young Sheldon season 6, Georgie's years of teenage rebellion are over already. Meanwhile, it is unlikely that Sheldon will ever break bad (outside of his season 5 visit to a comic convention during Spring Break, an act that he considered the height of teenage rebellion). As such, Missy is logically the only character who could cause Meemaw's personality to change between Young Sheldon and The Big Bang Theory. Since Young Sheldon has not yet explained why Meemaw acted so differently in The Big Bang Theory, this storyline could be used to fill an inconvenient plot hole.
