You can pretty turn up to a local league cross race with pretty much any bike – it doesn’t have to be a cyclo-cross bike and many people start on a mountain bike.
Cyclo-cross racing is pretty simple: it’s mass start, first across the line wins. It hasn’t got the technical demands of mountain biking, so you shouldn’t be in the situation where you’re scared by something on the course, but also once you get to a certain level then you need to be able to ride technical sections fast.
Cyclo-cross racing is really accessible. If you turn up to a road race and get dropped in the first five miles then you’re going to be riding around on your own and that’s no fun. You can turn up to a local league cross race and I’m pretty sure, no matter what your level, you’ll find someone to race against. Once the race has started it’s always strung out to the extent that everyone is engaged in individual battles, whether it’s for first place, or 31st.