My advice to new guitarists and bassists is play how you want, but be aware of the consequences of your decision. In general, the world isn't going to change drastically for the small percentage of us who do things differently.
I'm mostly a lefthander except when it comes to bowling, swinging bats, and golfing (I'm not really into sports, so those things don't play much of a role in my life). I clearly recall the day when I started playing trumpet in the 5th grade and the band director saw me holding the instrument left-handed and said "You can't play it that way". I said okay, and switched to righty without giving it much thought. Two years later, I took up French horn and played it lefty because there's no other way to do it. Again, I didn't think much about it. When I started taking guitar lessons two years after that, I followed what everyone else in the class was doing and played righty. To this day, my right hand is still dumber than my left, but I manage. When I played guitar in a folk duo with a fiddler a few years ago, he once remarked that my right hand looked like it was in pain, yet my strumming sounded fine to his ears and he couldn't figure out how I did it. I think that unless you're completely ambidextrous, one hand always works harder than other and you just have to figure out how to deal with it.
My personal bass weakness involves picks. Fingerstyle has never been a problem, but when I hold a pick, I feel like I have to squeeze it to death or I'm going to drop it. The fiddler taught me how to hold a pick comfortably to play guitar, but it doesn't work for bass. As a result, I mostly play with my fingers and I'm okay with that.