I'd like to tell you that because the Instagram comment policy applies equally to everyone (non-employees and employees), there's nothing unlawful about it under the National Labor Relations Act. But with the current composition of the most pro-union NLRB in history and its equally pro-union general counsel, all bets are off. I'd have real concerns permitting a client to take this step under these or similar circumstances.
Employees have the right under section 7 of the NLRA to engage in protected concerted activity — to complain, between and among themselves, about terms and conditions of employment. This right includes the right to express an opinion in favor of unionization and against the termination of co-workers (allegedly) fired for supporting the union, and covers social media posts and comments. Section 8(a)(a) of the NLRA makes it unlawful to an employer "to interfere with, restrain, or coerce employees in the exercise of" those rights.