Scotland for Marriage, the umbrella group including the Catholic Church, Church of Scotland and Muslim communities, is calling on supporters to oust sitting MSPs if they back the legislation as it stands.
The group has drawn up a hit-list of 10 constituencies where it claims it has enough support to wipe out the sitting MSP's majority at next Holyrood election.
It will call on supporters to punish the MSPs at the polls unless they back a series of safeguards for teachers, religious celebrants and others who continue to oppose same-sex marriage on moral grounds.
A spokesman said: "This is not a threat, it is merely democracy in action.
"Our supporters are against same-sex marriage. These MSPs have already indicated they are inclined to back the legislation.
"However, there is a long way to go and it is crucially important that our politicians are aware of the amendments which are required to provide sufficient safeguards for ordinary men and women in this country who support traditional marriage and who may be penalised simply for speaking out against same-sex marriage."
Seven of the target seats are held by SNP MSPs and three by Labour.
Those coming under pressure include Bill Kidd, the SNP MSP for Anniesland, whose majority of seven is outnumbered by the 1185 people in his constituency who have signed a Scotland for Marriage petition.
Also targeted is Labour's Duncan McNeil, whose 511 majority in Greenock is outnumbered by 917 local Scotland for Marriage supporters.
The campaign against gay marriage campaign is demanding MSPs back amendments to the Marriage and Civil Partnership Bill guaranteeing people who oppose same-sex marriage will not face any discrimination.
Tom French, policy coordinator for the Equality Network, which has campaigned for same-sex marriage, said; "All the polls show that the large majority of people across Scotland believe it's time LGBT people had full equality, including an equal right to marry the person they love."
"Introducing equal marriage is the right thing to do for a fairer and more equal Scotland, and with widespread public support it's also a vote-winner.
"That's why all the party leaders, and the overwhelming majority of MSPs from across the political parties, voted in favour of equal marriage."
MSPs backed the Bill by 98 to 15 with five abstentions in a preliminary vote last month. The legislation is expected to be approved next year.