Dr Anthony McRoy said certain interpretations of Sharia law could allow segregation, domestic abuse and rape.
Mr McRoy also called for the government to increase intelligence, border controls and defence spending to combat extremism.
His comments came after the Home Secretary Theresa May gave a speech on how government and British society could tackle extremism.
Dr McRoy told Premier: "We must not surrender the neutrality of the public place. What goes on in the mosque is the mosque's rules, what goes on in the public must be the public's rules. And I think it's essential that she's taken a strong stance on this.
"We do face a threat... from people who've gone to join them [Islamic State] and may come back, and that means really we have to beef up our intelligence services, we have to very strongly beef up our border controls.
"In the light of our very severe defence cuts... Islamic State and their supporters will have seen this and they realise they that with severe defence cuts Britain is at risk, and they can actually exploit this in different ways."
In her speech, Theresa May said government alone could defeat extremism, but that individuals, families and communities needed to denounce and report it too.
The Home Secretary said Britons have "rights as well as responsibilities" and rejected an "anything goes" culture, saying Britain's fundamental values are: "regard for the rule of law, participation in and acceptance of democracy, equality, free speech and respect for minorities."
Referencing her own Christian faith, she also said the speech was not an attempt to attack Muslims, but to say extremism has absolutely no basis in Islam.
Theresa May outlined some of the measures that would be taken to combat extremism, if the Conservatives win the general election in May:
- A review on Sharia law courts
- "Closure orders" for places used or owned by extremists
- A review of weekend and evening schools, which are currently unregulated
- A review of how the police deal with crimes committed to protect the reputation of a family or community, female genital mutilation and forced marriages
Listen to Dr Antony McRoy speaking to Premier's Des Busteed on the News Hour: