Laws passed this week decriminalising abortion in the state include "access zones", where it will be an offence to harass, protest against or film people visiting clinics.
Christian groups say they might consider a High Court challenge, arguing the legislation restricts a right of protest implied in the constitution.
At least one constitutional lawyer has warned a challenge could be successful.
But Pro Choice Tasmania's Jenny Ejlak says the issue was considered by lawyers consulted during the drafting of the bill and by the debate in parliament.
"All it does is have a little area of 150 metres where they just can't do those things in that particular geographical location."
Protests outside clinics are rare in Tasmania but more common in states such as Victoria, where a security guard was shot dead by an extremist in 2001.
Ms Ejlak said the zones were important for the privacy of women using a clinic.
"It's difficult enough to walk into a clinic that's in the middle of the CBD, hoping that none of your friends or workmates see you," Ms Ejlak said.
"But if there's someone standing outside taking a film of you on their iPhone and you think 'that's going to be all over the internet, I'm going to be labelled a baby murderer', that kind of intimidation is used as a tool to increase stigma, increase shame, decrease the likelihood that women are going to want to access the services that are available."
Businesses near clinics also support access zones, Ms Ejlak said, because protests affect their patronage.