First of all, Bollywood isn't synonymous with the Indian film industry as a whole- it's merely the centre of the Hindi-language film industry. The reason it's so prominent is that Hindi is the lingua franca of North India and is widely understood in South India too. The Tamil film industry is also massive with the Telegu and Malayalam film industries also being powerful in their own right along with a whole lot of others. In many ways these are separate filmmaking traditions- they developed in parallel to Bollywood and don't always follow it's conventions. For example, the Malayalam film industry (as befits that of a socialist state) traditionally tends to specialise in realist dramas and art films* as opposed to the "masala" tragicomedic melodramas that Bollywood tends to prefer. The Tamil film industry, on the other hand, is traditionally very much more action oriented.
Azander: It's a fallacy to assume that film would be regarded as "Western culture". The invention of the movie camera was, of course, Western, but the Indian film industry developed in parallel to that of the West. The first Indian feature film was shot in 1913 and the Indian film industry's birth was contemporaneous with the rise of Hollywood. There's no way that it can be painted as a decadent Western custom- a government of the sort you outline might well condemn Western films but they would be likely to then promote the local film industries even more.
*Your typical Malayalam film of the 80s would involve a hardworking village boy coming back home after labouring in the Gulf states for years. With his relative wealth he thinks things will look up but inevitably corruption, family troubles and other issues will combine to rob him of his hard earned money. The film closes with him saying goodbye to the girl he has futilely courted and can no longer afford to marry as he sets off once more for another few years of labour.