Category C doesn't mean "bad", it just means sufficient research hasn't been done to move it up the list to B or A. Considering the flu vaccine changes annually, I doubt it will ever be able to be moved out of the Category C range, but, in general, the flu vaccine is considered safe. They just can't test it fully enough each year to give it a higher ranking.
Obviously, getting the flu shot or not is a personal choice, but I've gotten the flu shot every time I've been pregnant before and my kids get it. I trust the doctors and my own experience has given me no reason to worry about it.