In these days unfortunately you cannot separate those things that easily. If you support or are on Russias side you’re by definition also on Putin’s regime side as everything Russia does is after all on his regime command. The war is entirely of Putin’s making there would be no war if not for him, and Serbia stand by his war, they are supporting him just like North Korea.
Those Russians who did not support have fled the country about 1m in total. There about 30% Serbian population that doesn’t support it either, the rest unfortunately dos.