Allowing Tommy Robinson to join UKIP will give substance to claims the party is moving to the far-right, UKIP AM Michelle Brown has said.
Party leader Gerard Batten wants rules to be changed so the former English Defence League (EDL) activist can join, and has proposed members vote on it.
The stance is backed by UKIP assembly leader Gareth Bennett.
Mr Batten said North Wales AM Ms Brown was "ill-informed" and wrote to members that Robinson would be an "asset".
South Wales East AM David Rowlands added he did not think Mr Robinson should be allowed to join, saying the former EDL leader joining UKIP may encourage members to leave the party.
Ms Brown said she is surprised "any Welsh politician" would support Mr Robinson, whose real name is Stephen Yaxley-Lennon.
Currently the party has a blanket ban on former members of the far-right British National Party and the EDL - meaning the anti-Islam campaigner is barred.
The party's ruling body, the National Executive Committee (NEC), is expected to discuss a proposal on Sunday for a party wide ballot on whether the activist can be specifically allowed in.
In an email to members Mr Batten said Mr Robinson would be an "asset to the party".
Ms Brown is not opposed to the ballot in principle, but said: "Allowing this former BNP and EDL member to join would be a gift to our opponents, who for once would have some substance behind claims the party is moving to the far-right."
Mr Robinson has criminal convictions for assault, drugs offences and fraud, the AM said.
"Even without his BNP and EDL past, he is not suitable to be a UKIP member," Ms Brown added.
Mr Rowlands said Mr Robinson's membership could lead others to leave.
"There are a number of members in the party that do not want him to be included," he told BBC Wales.
Gareth Bennett, who has recently replaced Ms Brown as a voting member of the ruling body, said: "It's absolutely right that UKIP party members should have their say on this issue, and I for one support Tommy's wish to join the party.
He added: "As Gerard Batten has said, we in UKIP have a unique opportunity to transform into a mass movement truly representing ordinary people."
Mr Batten said Ms Brown was "entitled to her view, but I think she's entirely mistaken and ill-informed."
Gerard Batten, who was appointed to the role in April and is known for making controversial statements on Islam, has said the party should become "radical" and "populist".
He was recently accused by former assembly leader Caroline Jones of moving the party to the far-right.
One party source, who said they could not be in the same party as Mr Robinson, described the potential ballot as a "referendum on Gerard Batten".
In response to Ms Brown, a spokesman for UKIP Wales said: "Nobody is proposing that we change the party rules unilaterally; it's simply about whether the members which to give the NEC the ability to make a one-off exception to the rules in this case."
Allegations of contempt of court against Mr Robinson were recently referred to the UK government's most senior legal advisor, the attorney general.
Ms Brown was excluded from the assembly without pay for a week earlier in 2018 as punishment for using a racial slur about a Labour MP.