Using a definition of inclusivity here without a consideration for power dynamics between the parties involved is totally uncharitable: as you've observed in your comment, there is no barrier to actually denying "exclusive rights" to activists, so it's more a matter of respect to the people who want to use the symbol (e.g. the pride flag, which few people have issues with it being used to exclusively represent LGBT groups) to make their cause more visible, rather than a lack of "inclusivity".