Last week, I had to change the time of a free community strategy webinar by one hour.
A few people e-mailed me with abusive messages.
Our approach in this situation is pretty consistent. We block their e-mail address and unsubscribe them from any of our mailing lists. We don't engage with abuse.
Over the past five years, I've unsubscribed several hundred people. This has saved me hundreds of hours in trying to placate individuals I probably won't like and a lot of mental energy. This has freed up my time to organize events/webinars, publish books/ebooks, keep the blog going, and otherwise do important work.
Any minute I spend on these people would be a minute I can't spend on high impact activities. Too often, community managers hesitate about removing members. They try to placate members or convert unhappy members into happy members.
Remove them quickly. Focus on the members that do want to be there. Focus on the members that are worth your time. Your time is limited/precious, don't waste it on the poor quality members.
For organizations, you might lose a customer if you do this. However, you will have more time to recruit new members, undertake activities that benefit the community, and broadly increase the ROI of the community. That's a good trade to make.
There are two other benefits here. First, the likelihood of receiving abuse falls as your zero tolerance policy becomes known. Second, the people you remove will most likely to join the communities most similar to yours (i.e. your competitors).
p.s. Relevant blog post from Seth.