The threat comes ahead of a meeting on December 19 when the incumbent board seeks to repel moves by a group of requisitioners to make changes into how the club is run and by who.
The Sons of Struth yesterday emailed Rangers shareholders, including Mike Ashley with whose company the club has signed a retail agreement, to "make clear that if all existing board members are not removed at the AGM we will use fan power to stop buying Rangers products, including strips and other products".
Mr Ashley's Sports Direct company agreed a deal with the club, under the then leadership of Charles Green, to sell merchandise at his stores.
The Sons of Struth, named after the legendary Rangers manager Bill, will also protest before tonight's league match with Forfar Athletic at Ibrox.
A statement from the group stated it was still not happy "with the corporate governance, business acumen or trustworthiness of the current board of directors". It added: "We can not support them or their aims."
The group, which claims it has strong support from other fan organisations, says it will continue its campaign up until the agm and added: "If after the current board are still in place then we could as customers stop buying season tickets, match day hospitality, club merchandise, match day catering and match day magazines. We have faith in the shareholders to do the right thing at the agm."
The statement lists the Rangers Supporters Assembly, Rangers Supporters' Association and the Rangers Supporters' Trust as among the bodies "who agree with the aims of the Sons of Struth".
However, any boycott would be a significant escalation of protest and it is unclear how fully that would be supported by fans.
The requisitioners, led by Jim McColl of Clyde Blowers, seek to have four nominated businessmen elected to the Ibrox board at the agm and are specifically urging the removal of finance director Brian Stockbridge.
Ally McCoist, the Rangers manager, has appealed to fans over setting off flares at matches after the pitch at Falkirk was damaged on Saturday.
The Scottish Football Association has called for an investigation after the synthetic surface was burned by a flare launched from the stands after the final whistle of the Scottish Cup fourth-round tie, a game Rangers won 2-0.