Mr Walker was left "upset" and "intimidated" at messages he received calling him a bigot after he supported a parliamentary motion stating no-one should be forced to approve of same-sex marriage.
The motion, tabled by John Mason MSP, made headlines after Alyn Smith, the first openly gay SNP Parliamentarian, criticised its supporters as "bigots".
Mr Walker said, "I'm very upset about it. I feel I've been intimidated and almost threatened.
"I have been called a bigot and all sorts of names, saying I live in the dark ages.
"The irony is I got married a few weeks ago. Needless to say it was to a woman!
"There are things called civil partnerships, which I accept, but I'm really concerned about the use of the term 'gay marriage' because to me it's a contradiction in terms and anything that puts homosexual relationships as any way equal to male-female marriages is just not right."
Mr Mason tabled the motion last week ahead of the Scottish Government's public consultation on equal marriage.
The signatories say that the distinction between marriage and civil partnerships should remain.
SNP MP Pete Wishart wrote on Twitter, "John Mason's nasty little anti-gay marriage motion is just wrong."
Mr Walker said, "I supported it because I thought it was a fair motion.
"When you read it word for word it's innocuous. We get dozens of these motions a week and every one goes through 'for' and 'against' pretty routinely.
"The reason it has boiled up into an issue is because (MP) Pete Wishart questioned it, then (MEP) Alyn Smith.
"Interestingly I've not been contacted by any other MSP about this.
"People who have been contacting me from various, I would have to call them gay rights organisations, have sent me emails that have been highly abusive. I regard it as bullying.
"It's like they are trying to stop free speech."
Mr Walker said his membership of the Church of Scotland did not affect his decision about the motion.
"That has nothing to do with it because I regard it as a fundamental moral issue concerned with the definition of what marriage is.
"I don't think people, whether they are registrars or ministers, should be forced into agreeing to do something they don't morally agree with."
A Facebook site was launched by people furious at Mr Mason's motion.
'Oppose John Mason's Homophobic Motion' is reported to make reference to some of the Shettleston MSP's supporters, including Bill Walker, saying,
"Never mind, with the NHS cutbacks, they'll be dead soon."
Green Party leader Patrick Harvie is quoted in a national newspaper saying, "I doubt the good people of Dunfermline knew they were electing a bigot on this scale, and the SNP leadership must be anxious about the damage the likes of Mason and Walker are doing to their reputation."