Stuart Burke, who led the Milton Keynes licensing committee, will be on a group that holds the council to account.
Subhan Shafiq, who resigned as mayor because he vouched for the driver, will be on two committees.
Their party, the Liberal Democrats, said it must be "proportionate".
It emerged last month Nadeem Ahmed Kiani, who raped and sexually abused prostitutes in London in 1994, was granted a private hire taxi licence in 2011.
Terry Baines from the Fishermead Residents Association said the Liberal Democrat group on Milton Keynes Council had shown "contempt" for residents and the leader should "get rid of them as councillors".
"When is [Liberal Democrat leader Douglas McCall] going to grow a spine and look after the people of Milton Keynes?" he asked.
Mr McCall said the councillors had "made decisions that we have difficulty understanding" but the party had to "be proportionate".
"We need to remember they haven't broken any law, they haven't broken any rules of the council," he said.
Kiani's taxi licence was suspended in 2012 when Thames Valley Police revealed details of the offences to the council - but the suspension was lifted in the same year.
In March, he was given a hackney carriage licence by a council officer.
Last month, an investigation resulted in both of Mr Kiani's licences being revoked and the resignations of Mr Shafiq, licensing committee chairman Mr Burke and deputy chairman, Gladstone McKenzie.
Mr Burke will now sit on the overview and scrutiny committee, while Mr Shafiq will join the health scrutiny and joint negotiating committees.
Mr McKenzie will not take up a new role.
An ongoing council investigation into taxi licensing has found seven other drivers in the city have criminal convictions.
Two councillors who resigned from senior posts after a rapist was granted a taxi licence have new been given new local authority roles, despite residents' calls for them to step down.