Many different people would probably provide you with many different answers.
While many people do jump obstacles on trails or play around on fun days, etc. in western tack, that is certainly different from learning the proper techniques to jump for pleasure or competition. Purists would argue that even a so-called "western bit" would not be acceptable for jumping, but the harshness of the bit also depends upon the rider's hands. Jumping with split reins could certainly be a safety issue. The biggest problem would be with a western saddle which simply wasn't designed for jumping, so it could be a major safety issue for the rider.
