Can I race cyclocross or road races without using clipless pedals any cycling specific shoes?

A. Clipless pedals, cleats, and cycling specific shoes are expensive.
B. I am not trying to be the best cyclist in the world. I only want to compete in entry-level cyclocross and road races for the purpose of fitness and fun.
C. I have had some scares with clips and straps. I am am afraid I will have the same experiences with a clipless system, even easy to use ones like Speedplay frogs & Shimano Click'R.

I realize that I will lose efficiency in my pedal stroke by not using a clipless system, but I will train harder to compensate for that.

Can I compete in cyclocross racing or road racing without clipless pedals and cycling specific shoes?