Is there a sin or burden of wrongdoing in removing a member from an entertainment group on Facebook without them having committed a violation, merely due to personal disapproval, and will this result in being subjected to similar injustice?

If you own the page, you have the right to delete whoever you wish and add whoever you wish. Friendship on Facebook is merely a follow, and the rules of connection and estrangement do not apply to it. However, if you manage the page by prior agreement, then deletion and retention depend on the agreement. Your choice should be for the benefit of the page, not for your personal benefit, and you do not have the right to delete someone merely because you dislike them. It is advisable to save time and not waste it on what is of no benefit.