Why should the work stop?
In the Old Testament, Nehemiah was rebuilding the wall around Jerusalem (a great work). His enemies entreated him to leave the work and come down to talk to them but their motive was to simply do him harm.
Nehemiah's reply to his enemies? "I am carrying on a great project and cannot go down. Why should the work stop while I leave it and go down to you?" (Nehemiah 6:1-4)
Your enemies will probably never change. Answer them with an adamant "NO" and get back to the great work to which God has called you.