Is it bad to cut onions and other vegetables on the same cutting board?
No it isn't bad.

It's all a matter of flavor. I don't really mind getting some onion juices into my next dish, unless I'm making something sweet like fruit salad - in this case I would rinse the board before moving on.

My advice to you about boards is: Get yourself a proper wooden or bamboo board or butcher's block, treat it with care (clean it an soak it with mineral food grade oil every now or than...) and that's all you'll even need.

I've been using my favorite board for over 10 years now. And it doesn't smell of onions.