In Avengers: Age Of Ultron, the newly-born Vision gained the trust of the Avengers after picking up Thor's hammer, Mjolnir, a feat that can only be achieved by those who are deemed worthy by Odin. But with Vision's body being reanimated as the Mind Stone-less and robotic "White Vision" at the end of the Disney+ series WandaVision, things have changed drastically for the synthezoid.
With that said, let's look at whether WandaVision's White Vision could, like his predecessor, lift Thor's might weapon.
Why Vision Could Lift Mjolnir
There are three main trains of thought when it comes to theorizing why Vision could lift Mjolnir, one of which is that since Vision is a machine, he is able to lift the hammer as there is no "life" to judge worthiness upon. This is possibly negated, however, by the fact that people have been shown failing to move Mjolnir despite using advanced technology. An elevator or a coat hanger could hold and transport Mjolnir, though, since it appears that the ability to use it is based on whoever is operating the technology.
This leaves only the second theory: Vision was indeed truly worthy, either by virtue of the Mind Stone that was implanted in his head, or that he was just born and was a pure soul at the moment. While Vision is, in fact, a machine, Odin's enchantment would likely detect sentience and intentions to judge worthiness, meaning an evil robot like Ultron would not have been able to wield Mjolnir. Within this theory, there are also some who suggest that the Mind Stone is what grants him both sentience and worthiness, but that might not exactly be the case.
Vision Doesn't Need the Mind Stone to Be Worthy
In WandaVision, it was revealed that the secretive agency S.W.O.R.D. rebuilt Vision but without the Mind Stone. However, it was theorized by Bruce Banner in Avengers: Infinity War that there could still be a lot of Vision left if the stone was taken out, given that parts of Tony Stark, JARVIS, Ultron and him were used to create Vision's AI. In short, Banner's theory suggests that the "best parts" of Vision should still remain.
White Vision appears to be sentient but controlled under the influence of S.W.O.R.D., proving that he can be a sentient being without the Mind Stone, but those parts that Banner mentions are probably still locked away. At the end of the series, it appears that Hex Vision unlocked White Vision's memories, effectively reverting him to his former self, but the ramifications of that remain to be seen.
Hex Vision Could Be Worthy
From what audiences have seen of White Vision so far, he appears to be a soulless shell of his former self, albeit with his old memories seemingly returned. While he does appear to be sentient, his rewired programming as a weapon for S.W.O.R.D. could leave him unworthy as Odin's enchantment seems to base worthiness on both selflessness and ability to keep one's intentions pure. That is not to say that White Vision could never be worthy again, but in his current state, he is not acting as a selfless hero.
Hex Vision, on the other hand, may just be worthy of the hammer if Mjolnir ever found its way into Westview. Throughout WandaVision, Hex Vision selflessly faced likely death in a failed attempt to warn the outside world to help the townspeople and protected Wanda from his White counterpart. At the very end, he was also willing to part ways and "die" to set everyone free and turn things back to normal. His selflessness is obvious, and based on previous cases of "worthiness," Hex Vision certainly fits the criteria, making him the more likely candidate to wield the hammer.
Written by Jac Schaeffer and directed by Matt Shakman, WandaVision stars Elizabeth Olsen as Wanda Maximoff/Scarlet Witch, Paul Bettany as Vision, Randall Park as Agent Jimmy Woo, Kat Dennings as Darcy Lewis, Teyonah Parris as Monica Rambeau and Kathryn Hahn as Agnes. The series is available to stream on Disney+.