Ben Horowitz has the answer: no... you should not.
A good rule of thumb is the reflexive principle of employee raiding which states: “if you would be shocked and horrified if company X hired several of your employees, then you should not hire any of theirs.” The number of such companies should be small and may very well be zero.
It is important to note that just about all of these kinds of policies violate the Right to Work laws in California. Specifically, if you block a hire based on this kind of policy and the employee loses their job and cannot find work, your company is liable for his wages. As a result, the business relationship with the other company must be extremely important for you to employ any kind of “hands off” policy.
This is a good article to have read before you find yourself in such a situation.