Action for Blind People offers support services for blind and partially sighted people in England, and has had an association agreement with the RNIB since 2009.
Unison has today gone public with concerns about the change, which is set to take place under the Transfer of Undertakings (Protection of Employment) regulations, known as Tupe, on 1 September this year, after talks with the RNIB.
The affected staff work for the RNIB in Scotland, Wales and Northern Ireland, and for the RNIB helpdesk in England.
Unison and another union, Unite, are recognised by the RNIB, which employs 1,896 staff, but not by Action for Blind People, which has 357 employees.
Simon Watson, national officer for the community and voluntary sector at Unison, told Third Sector that the charity had said the transfer would improve services for users, but he felt it was not "being straight" about the reasons for the change.
"Why change the employer of hundreds of staff when you’ve already got two organisations that are supposed to be working closely together?" he asked. "What will that do to improve the service you can’t do by changing it inside RNIB? It feels like there’s something not being said. We just want a good clear answer that will put people’s minds at rest."
In response to Unison’s concerns, the RNIB told Third Sector the rationale for the transfer was to bring all the regional teams responsible for service delivery into one place under the same structure and the same direction.
A spokesman for the RNIB said the charity was "in positive talks with the trade unions about what this transfer means for the collective bargaining unit and recognition agreement".
He said: "We want to reach thousands more blind and partially sighted people who we aren’t reaching at the moment, and we believe this change will help us to deliver this. These changes are based on the views shared by customers on how we can provide a better service."
The RNIB recognised Unison and Unite late last year after staff voted in favour.
Watson, who said Unison had "hundreds" of members at the RNIB, said strike action was not a consideration at this time.
Unite, which disclosed that it had 139 members at the RNIB and 20 at Action for Blind People, was unable to say whether it supported Unison’s stance at the time of publication.