Which borders would that be? Russia doesn't share a border with Syria, nor Afghanistan or Iraq, nor any other country the US has invaded in recent history.
Russia is quite capable of destabilizing their own borders with, Ukraine, Georgia & Estonia.
Now if by destabilize you mean NATO "encroaching" on their border, I'd argue that it does the exact opposite, it stabilizes the border because it's become readily apparent in Ukraine how "stable" borders with Russia are and what happens when a weaker nation doesn't follow the orders from Moscow.
No, Russia is the destabilizing factor on Russia's borders.