To clarify the belief that was cultivated through propaganda is that there are reckless Nazi groups in Ukraine who stop at nothing to hurt russians. They were striking at ethnically russian regions of Ukraine for last 8 years. When Russia invaded to fight these groups they positioned their forces in the hospitals and schools. As they strike back they are hitting their own schools and hospitals mostly from being sloppy, because that's what they are and the equipment is old. And in some cases maliciously, because they need gruesome content for the west. Russian forces are doing precision strikes and hurt no civilians.
I think you underestimate how massive and elaborate Russian propaganda is. These stories are fed in pieces over weeks, sometimes years. For example it took multiple years to establish and cement the idea of Nazi groups in Ukraine. Now if you start at this belief it's not that far fetched to believe these groups have no regard for human life whether it is their foreign or their own.