Which is why France and the UK were also obliged to declare war on the USSR, but they didn't.
They were not obliged to. However, the fact alone made a land campaign against the Germans quite hopeless, as well as the only success being more territory lost to the USSR. Bear in mind that the USSR took their pre-planned slice of Poland (Molotov-Ribbentropf pact) as well as the Baltic states (Estonia, Latvia, Lithuania).
Between the western nations there was also a disagreement about Nationalism and communism. Which was the worse one? Both France and Britain had quite som on-going communism at the time. The USA was however very suspicious towards communism. Churchill however was clear about Nazism clearly being the worse of two. Then there was the chance of the two baddies going against each other, -which did happen....