People always talk about consistent display of spaces whereas tabs might be shown as 4 spaces or even 8. Of course that means you can usually customize how tabs are rendered unless you code in Notepad or something crazy.
Lots of people need to access files on a server via Emacs or Vim. Having to deal with tabs there can be very frustrating.
On vim (I am sure as hell you can do this on Emacs) you can always define your tabs to be spaces and you can specify exactly how much. So this is really not a big problem.
I'm not an Emacs guy but it's trivial to set the tab size on vim. I would be shocked if that were not also the case for emacs.