We humans, even hardened atheists, are all prone to some form of cognitive dissonance or the other. In fact, without some kind of contradictory belief systems within us, it’s hard to survive. It was probably integral to our survival in a Darwinian sense as a species.
The historical Yeshua, for instance, was probably an Aramaic speaking Jewish Rabi who considered himself a prophet like Moses, Elijah and others. Yet, centuries later, folks made up his birthday to coincide with other pagan religious festivals, integrated Yuletide and other pagan traditions, Christmas gifts, snow, White Christmas, Santa Claus, Easter Bunny, Easter egg, why they even created a blonde haired Caucasian Jesus… So many things that has objectively nothing to do with the historic figure of Jesus. Same with Muhammad. Same with all other religious beliefs.
That’s human beings. Our brain finds it very hard to separate fact from myth, in fact we integrate the two to create a sort of hybrid reality.
Yes, the most ardent Modi supporters believes his economic moves are ‘capitalistic’ even though they can only be described as ‘Stalinist’ and far left. But that’s all part of the human experience. Yes, most of the stuff created around the mystique of Gandhi is probably all mythical
So, factual accuracy, is important depending on what you are trying to achieve. Especially if you are trying to achieve factual accuracy! For most other purposes, it matters little, I guess. That’s the human animal for you, in my view!