Russia is not exactly “pro-Israel”.
Russia has interests in the area, and Israel is trustworthy and not insane. Sanity counts for a lot, even when you may disagree.
That said, Putin, while very much a nationalist Russian, is not anti-Semitic. He had a difficult childhood, and several neighbors and teachers (who happened to be Jewish) stepped in and acted as paternal/maternal figures.
Russia seeks to advance her own self interest, like any rational nation should. If stability in the MidEast is in Russia’s interests, then she will seek to maintain stability. Putting the despicable Obama regime in a twist is a free bonus.