As a player I appreciate other players and what goes into becoming one. Having said that I also appreciate a DJ chopping sounds into tiny pieces to create something completely new. There is a direct comparison between those 2 people. What you call them is beside the point.I hear you but the OP's question was, "Are DJs musicians?"
I understand the advantages they may have. But they are a crop of people that are taking advantage of technology at the expense of the working musician. I've lived to watch and experience the transition. They are not musicians. They haven't learned how to play a musical instrument or studied as a vocalist. I can't place a DJ in the same catagory as a musician.
In my mind, there is nothing finer than live musicians.
As a player, I'd hope you feel the same.
The other type of DJ, the one who just plays the records people want to hear, I wouldn't consider a musician at all. But s/he operates in venues where, to be frank, chops don't mean poopie. They provide an excuse for women to dance and men to try to buy them drinks. Technology was always going to take over that job. Of course, that little game will be played for the foreseeable future. Nothing to stop the underemployed musician grabbing their laptop and making a buck on the side with their knowledge of what the people want to hear.