Can You wear brown shoes with a navy pinstripe ...

You can wear whatever you want. There's no law against wearing navy stripes and brown shoes.

Rules of fashion, however, tend to consider all shades of blue as incompatible with any hues of brown, so if you want to be mainstream, it's probably better to go for the black shoes.

Good taste would require you to wear black shoes especially for semiformal occasions. On those occasions brown is never worn.

You can certainly wear brown shoes with navy pinstripe.  If it makes you feel better, add something else brown to the outfit and it'll be fine.  One of the things I've learned from watching too much "What Not to Wear" on TLC is that shoes do not have to be the same color as the pants/skirt you have on. 

I'd try to stay away from putting navy and brown together... they make sort of a nasty combination.  Stick to black if you can.  It looks a lot better and you can wear a black belt to match the black shoes... looks nice. 

black

A Classic - Black shoes with a Navy Suit will never go out of style.  On the other hand you can also wear a brown belt and brown shoes.