On LGF, it said protest organisers estimated 200,000 thousand people at the one in San Francisco. Aerial photos show about 65,000 peak. (Source Here)

How should we explain the protestors ignoring the facts? I suggest my anti-theory explantion: because they are more focussed on their cause then on morality. And they think lying will further their cause.

And in a direct sense, it's hard to tell. Lying has advantages (because people will think the ideas are more popular than they are) and they disadvantages (because people will get annoyed with their exaggerations and stop listening). And thus, calculating whether to lie, based on how it furthers their cause, is at best, an expensive calculation prone to error. Not at best (and in reality), their approach is, even in the limit, divergent from morality aka wrong.

If we just look at the morality of the situation, though, it's easy. They are attempting to mislead and manipulate people. End of story.