Party bosses last week withdrew all support for Neale Hanvey, who was selected by the Nationalists to fight the marginal seat of Kirkcaldy and Cowdenbeath, after questions were raised about messages posted on Facebook.
The former leader of the SNP group on Fife Council will still appear on ballot papers in the constituency as the deadline for nominations has passed.
Mr Hanvey is now campaigning as an independent candidate in the hope of unseating Labour's Lesley Laird, who is defending a majority of just 259.
The First Minister on Monday called for local SNP supporters to instead campaign in neighbouring seats, stressing her party “unfortunately” no longer has a candidate contesting the seat.
But that call has been ignored by George Kay, one of Kirkcaldy's most senior former SNP councillors, who has said he will go against his party.
Mr Kay - who first joined the Nationalists in 1975 - described Mr Hanvey as an "excellent" candidate and the allegations against him as "absurd".
"The party has been forced to take action against him on the grounds of antisemitism," he told the Fife Free Press.
"Not only are these charges absurd but behind them are other motivations which are much more sinister and led by a darker group other than the SNP.
“I hold no problem with the party having to take the measures it did, but I hope in the subsequent enquiry every aspect of this situation will be considered.”
Mr Kay told the paper, a sister title of The Scotsman, that the “honest thing” was to “weigh my party membership of 45 years against the need to see a dedicated, responsible person represent us at Westminster”.
He added: “I can think of no better political ambassador to carry forward the spirits of those candles to the constituency, to Fife to Scotland and to the world."
Other independence supporters have been vocal in their support of Mr Hanvey. One, Alex Gallacher, posted on Twitter this week: "I will say again I support Neale Hanvey and would ask others to do so. How can we disenfranchise SNP supporters in a winnable seat?"
A prominent pro-independence blogger, Peter Bell, last night claimed the SNP owed Mr Hanvey "a measure of loyalty".
"I don’t live in the Kirkcaldy and Cowdenbeath constituency," he wrote in a blog. "I don’t know Neale Hanvey. It’s not for me to judge whether he might be the best MP for that community.
"But, having pondered the other issues, I cannot in good conscience do other than agree with George Kay. There is something not right about this whole affair. And Neale Hanvey deserves the benefit of any doubt."
Mr Hanvey admitted to having shared an article from the Kremlin-backed news agency Sputnik from 2016 concerning the Hungarian financier George Soros, illustrated with an image showing him holding puppets of world leaders.
An investigation into Mr Hanvey’s actions has been launched by the party. Asked this week what would happen if he won the seat, Ms Sturgeon said: “He’s suspended at the moment, there’s disciplinary action that will flow from that and it would not be appropriate for me to comment while that’s ongoing.”
Ms Sturgeon also addressed speculation Mr Hanvey may have been axed because of his views on trans rights. She said: “He was suspended because of the antisemitic comments he made and that is the long and short of it.”