War makes people angry, and angry people are trivially swayed by propaganda.
For example, there's thousands of people still screeching online that the US deliberately bombed little girls in Iran. No, they hit a girls school by accident, it used to be an IRGC military base building and is surrounded by IRGC buildings!
I don't condone Israel's actions in Gaza, nor do I condone the US/Israeli attacks on Iran.
Having said that, it's important in a war -- irrespective of what side one is supporting or opposing -- not to believe exaggerations or outright lies.
War is bad enough, we don't have to sprinkle imaginary horrors on top of the real ones!
In the worst case, if too many people spout transparently obvious propaganda, then that discounts the believability of the true horrors. This is most obvious today with the "that's just a fake AI video" retorts, but before it was "fake news", or whatever.
Diluting the truth harms it.