The only "opt-out" clause in the bill is one which would allow the local sheriff to go before the county board and ask that he not be required to sign applications. The county board would have to reach a two-thirds majority in order to authorize the sheriff's request.
That doesn't mean that residents of that county cannot get permits, though. They can go to another county where the sheriff is signing applications. And, considering that the sheriff's department will get $90 per applicant (less the approximately $7 cost of the NCICS check), a sheriff who wants to refuse is an idiot.