Munich with non meat eaters
You have 2 choices (I have the same issue):
Indian: Swagat (we've tried the rest together, and this was the only one my friends were happy with)
Vegetarian: You have 2 choices:
Zerwirk (last visit was 2 weeks ago - superb):
Feel free to google them all. Zerwirk has an organic chili sauce that they can give to your friends who feel that the food is... ...underspiced.
I ate well in Munich when I was a ovo-lacto vegetarian.
I agree with Joan that most restaurants will have at least one or two vegetarian selections. I usually stuck with spaetzle or Gemischter Salat (a selection of different salads on one plate, sometimes comes with a fried egg on top). Obatzda is a Bavarian spread made out of Camembert (but I'm guessing there's animal rennet in Camembert), paprika and a bit of beer, which is another lacto-veg option. Seems like pumpkin soup shows up on a lot of menus, too.
Make sure that your companion lets the waitstaff know that no meat can come in contact with the dish (ohne fleisch = without meat) because sometimes ham or bacon shows up unannounced in a dish.
In case you don't feel like eating German or Bavarian food, the Turkish and Middle Eastern places have lots of vegetarian options like hummus, spinach pies, cheese pies, etc.
Here's a very recent thread for an individual who was wanting vegetarian or fish places in Munich, which might be interesting to you :
I'm not vegetarian, but am quite aware that Munich has several good vegetarian restaurants and many of the non-veg places have a number of vegetarian selections. Even our hotel, which apparently did business lunches daily always included 1-2 vegetarian selections. So it should not be too difficult to at least minimally satisfy your vegetarian colleagues, even if it's things like spinach cheese spaetzle. I also noted several Indian restaurants and plenty of Italian.