No. The plot of RE is essentially episodic and simple enough that you really don't need to understand past game's continuity to keep up, and the plot itself is cheesy B-movie mania that almost never tries to deliver super serious plot points. All you need to know is Umbrella are an evil corporation that make and sell bioweapons.

It's an especially silly reason not to play 7/8, as those two entries are even more standalone. You can count the direct links to past games in 7 on one hand