If you're the manager, the simple solution is just to require it. If, for instance, the design team uses Illustrator and Photoshop and Sketch all for hi-fi, pick one and stick with it. People's feelings don't matter here; ultimately the goal is to make sure that the organization (and this team) can run efficiently. If that means that some members are going to have trouble initially, that's a small price to pay for the amount of time and effort you'll save in the long run.
I've been teaching UX and there are hundreds of different tools to use. Design teams (including graphic design and UI) are filled with people who live on individual tools/applications. For UX, the only tool I care about is my head and a whiteboard/paper. Everything else is for convenience. I'm intentionally tool-agnostic because there is no perfect tool, only the right tool for your team.
That said, both teams I've run I've instituted every tool, not just for the design team. Slack for communication (oh so hipster, before it was even out of beta), Sketch for hi-fi, Balsamiq for prototype, Lucidchart for IA, photoshop for marketing materials, Sublime for engineering (except for Xcode, stupid Apple), etc.
Part of being a manager is to manage the efficiency of the team.
That said, when you bring it to the given team and say that the switch is happening, if you explain why and that it's fine that efficiency will drop in the short run, most people are okay with that. Career-driven individuals may not enjoy the switch but they'll recognize that you're giving them another tool that they can put in their arsenal.
When I instituted Slack, for instance, both companies I did it at took convincing. Moving to Sketch was trouble, until my team actually went ahead and used it (and then they apologized because it's so great). And to be clear, it's not just for tools, the same works for processes. As a manager you can experiment with what works well and then formally move everyone to it. As long as you aren't mean/rude about it, good organizations will accept it and move forward.