I think Lady Jane Grey was more a pawn of those around her than anything else, because she had to be, of neccesity. She was an intellectual, but very young, and forced to do what she had to do to survive, which killed in her in the end. Her execution was unfair because she might have been a rebel, but it wasn't her choice. She never loved her husband, but after all, Hollywood turns many stories into love stories that were not to begin with.
It seems to me that Jane had the makings of intolerance in her, yes. She would not have been as tolerant as Elizabeth, not that many were. How much this would have developed would be interesting, but she would in some ways have been a queen of her age, but stronger, and more intellectual than most.