Two Celtic fan groups have urged the club to reverse their decision to decline tickets from Linfield - and asked the Belfast club to consider selling directly to visiting fans.
Celtic last week revealed that no tickets would be available for their fans for the potential Champions League qualifier at Windsor Park.
Should Northern Ireland's champions progress past La Fiorita of San Marino, the second-round first leg has been pencilled in for a 5pm kick-off on Friday, July 14 - two days after the Orange marching season hits its peak - following discussions with the clubs and the PSNI.
The timing exacerbated fears over a meeting between two clubs with supporters on opposite sides of Northern Ireland's political divide and the Scottish champions stated that the "safety and security of all Celtic supporters travelling and attending matches is of paramount importance to the club".
But the Celtic Trust and Green Brigade have demanded a re-think.
A joint statement posted on the trust's Facebook page read: "The vague statement released by the board late on Friday afternoon did not contain any clear explanation of this decision - a decision made with no consultation at all with fan organisations, groups or regular European away travellers.
"The statement noted 'safety concerns' but it is our understanding that the PSNI does not object to Celtic fans travelling and, indeed, Linfield has publicly encouraged the board to accept our allocation and stated they are 'more than happy' for Celtic fans to attend the match.
"We believe that the board is more concerned with protecting the brand than the welfare of the fans or the success of our team. It is a very sad and strange turn of events when the custodians of our own club do not want the world famous Celtic support backing the team in a 'crucial' away match yet the home club welcomes us with open arms.
"We call on the board to reconsider their decision, and should they fail to do so, for Linfield to sell tickets directly to Celtic supporters.
"Our away support has significant experience of dealing directly with host clubs in the distribution of domestic away match tickets and doing so again for the match in Belfast should be a straightforward process.
"This should be done in a fair, responsible and transparent manner and would avoid the scenario of ticketless Celtic fans accessing the home end, which may, in itself, lead to genuine safety concerns."