There has been lots of research done on this and studies show that engaging a "hater" is generally a waste of time and is what they want you to do in the first place. You're pretty much being sucked into a hole where no one is a winner and both parties end up looking bad.
However I also don't think it's smart to flat out ignore all criticism, if there are potential high value customers that are giving feedback there might be something to it (though you know your business better than anyone else and is up to you to decide). However it's definitely not worth engaging with people who are just criticizing and flat out don't know what they are talking about.
Either way you need to be careful how you spend your time, anyone whose seen the movie Jerry Macguire knows that