The English Defence League (EDL) has supported a Bournemouth councillor who said online that it was the only group that "sticks up for the English".
She also suspended herself from the Tory party and referred herself for disciplinary procedures.
Kevin Carroll, co-founder and joint leader of the EDL, said it seemed she had "bowed to pressure" from her party after expressing her views.
He said: "She wouldn't have said it if she didn't believe it in the first place, but she's bowed to pressure.
"There are a lot of politicians and MPs that feel the same way but are too scared to speak up."
The married grandmother, who has been a councillor for the Moordown ward in the Dorset town since 2007, posted the comment in a conversation.
It read: "But nobody else except the EDL stick up for the English."
The next day Ms Anderson issued a statement saying the comment had been made in haste.
She said it was made "without thought and without understanding the racist policies espoused by the EDL".
"I would like to make it clear that I in no way support the English Defence League or any other organisation that promotes intolerance," her statement added.
Mr Carroll said: "We're not banned, we're not racist, we're not violent. I don't know what she's talking about.
"But she would say that because she was probably guided. She's been leaned on to make that statement.
"I would say she's made that in haste, probably in more haste than the first [Twitter comment] and probably under pressure."
"It's brave of her to do what she's done. It takes courage to go against the grain.
"But I don't blame her for bowing to pressure."
Ms Anderson said she had suspended her own party membership and had referred herself to Bournemouth Council's Standards Board.
She said she would co-operate fully with the council's and her party's disciplinary procedures and would not make any further comment until investigations were complete.
Ms Anderson's Twitter account was later taken down from the site.