Fortunately it was pretty easy to make one of my mountain bikes ‘cross worthy, and that was enough to get me by for a few seasons. I think any cross-country oriented mountain bike will work for cyclocross racing, with a few caveats. A hardtail is best, but a full-suspension bike isn’t a deal breaker. It’s like bringing combat boots to a 5K run. The equipment will work, but will probably put you out of contention for a podium spot. That being said, I’ve seen some sub-20lb, super-efficient, “no-bob” full suspension bikes with traditional front triangle designs, which would be fine to take to the starting line.