Do not kill them out of hand.
First, check with Fish and Game and state law to see the status of hybrids. If you can't keep them, see if you have any wildlife sanctuaries that will.
As for those getting worried about them, Maine Coons are known to breed on the rare occasion with bobcats and the resultant offspring tend to be okay as long as they're socialized and trained properly.
Such hybridization which supposedly produced the Pixiebob breed is anecdotal.
The Desert Lynx is a known hybrid of Bobcat and domestica cat.
The people breed bobcat hybrids, you may want to drop them an email:
Bengal, Desert, Highland, Lynx, Jag, Bobcat Hybrid, Kitten, Exotic Cat, Designer
- Coeloptera