Campaigners against the council tax say payments from well-wishers should not be allowed.
Pensioner Sylvia Hardy: Claims council breached human rights
They say such payments infringe their human right to protest.
It has emerged councils are divided on the issue.
Exeter City Council accepted a cheque to pay protester Sylvia Hardy's bill last week, but Torridge District Council refused to accept donations after consulting campaigner Elizabeth Winkfield.
Both were refusing to pay, in a protest by the Devon Pensioners' Action Forum against the tax.
Forum leader Albert Venison said Exeter City Council had breached Ms Hardy's human rights.
"We are a bit angry about it really it takes away the force of the protest," he said.
"We'd like to be able to say 'thank you very much but we don't want you to do this because you're destroying our campaign'."
Exeter City Council said anyone could pay the tax.
It said in a statement: "The council has not infringed Ms Hardy's human rights. There is no right to a debt - this can be paid by anyone.
"As the collecting authority, our duty is to collect council tax as efficiently and as cost effectively as possible, and we owe this to all our council tax payers."
Elizabeth Winkfield: Payments were refused
Lindsay Ansell, the head of customer services at Torridge District Council, which refused to accept cheques for Ms Winkfield, consulted with the 83-year-old protester who made national headlines with her court appearance in February.
She said: "It was the first incident of its type and we decided to advise Ms Winkfield of the donations we had received and Ms Winkfield did ask us not to pay those into her account and so far we have not done that."
Ms Winkfield, from Westward Ho!, said: "They just asked me what I wanted to do with the money - did I want it paid into my account and I said 'no'.
"I said I am doing this as a protest, not because I can't pay for it and they knew that."
Elsewhere in Devon, Plymouth City Council and Teignbridge District Council will accept payment from third parties.
Mid Devon District Council has no formal policy, but would not accept a cheque if a council tax campaigner did not want them to.
Torbay Council says it would depend on circumstances and East Devon District Council said it had never needed a policy on this.