It is true that both Russia and West will act in their own interest. It is just that at this point of time, the West 's strategic interests are more closely aligned with India than with China or Pakistan. So, in their own interest, they will support India in a conflict against these countries - just like they will support Saudis against Iran, even though Iran is more of a democracy.
Similarly, India has more to gain with allying with the West than with a declining authoritarian regime in Moscow. Russia is now so weak that it can't help even its treaty allies like Armenia, with which it shares a common border, while Azerbaijan takes its territory. In fact, Russia is being forced to buy supplies from powers like North Korea and Iran even to fight in Ukraine.
If the Soviets supported India in 1971, it was because the two countries had a mutual defence treaty at that time, India had a socialist government, Pakistan was a member of SEATO and CENTO and the Sino Soviet split was firmly entrenched ( in fact Pakistan was facilitating a secret rapprochement between US and China). Moreover, the Soviet Union was a comparable military power to the United States with all of the resources of the Soviet Union and Eastern Europe unders its control and major allies all over the world. The situation today is very different.