In the UK I don't recall the public truly believing that Iraq actually had "weapons of mass destruction". The press had been calling the intelligence report the "Dodgy Dossier" https://en.m.wikipedia.org/wiki/Iraq_Dossier and I recall wide doubt on the famous phrasing of weapons being "launched within 45 minutes" https://www.theguardian.com/politics/2004/feb/05/iraq.iraq1 which it turns out referred to... conventional battle munitions like mortars.
It was an absolute shit show of lies that nobody really believed. A million people protested https://en.m.wikipedia.org/wiki/15_February_2003_anti-war_pr...
And still, the war went on as usual.
Even if 90% of Russians protested against the invasion of Ukraine I couldn't be sure it would make a difference.
As it is, most Russians don't even see this as a war, just a continuation of the ongoing Donbass conflict.