I'm off to Munich for a 3-day trip and I wonder what are some traditional vegetarian Bavarian dishes that I should not miss to taste? Is there any?
There is one dish typically found in most traditional Bavarian restaurants that indeed is vegetarian. It is not a traditional Bavarian dish but a traditional Swabian one, though.
This dish is called Käsespätzle, in Bavarian dialect it might also be written Kasspatzn. It consists of the traditional Swabian Spätzle (a type of noodles) with lots of molten cheese and optionally fried onions (both crispy and non-crispy although the former seems more common to me).
Furthermore, if you are into cold dishes or visiting a beer garden (Biergarten), you may also be interested in Obazden. This is most loosely described as a variant of cheese; more adequately it is whatever the kitchen had left over and is fitting to put into a creamy cheesy mixture. It has a strong taste and would typically be eaten with bread or pretzels. If you are in a part of a beer garden that includes service (especially note that in Munich many beer gardens are bring your own food), they will usually have pretzel with Obazdem on their menu.
Note that the spelling of Obazda is not fully fixed as it is a dialectal word. Note also that since it is grammatically a nominalised adjective (deriving from a past participle), it features a not-so-common (for nouns) declension which is frequently done wrong by non-Bavarians (‘Prussians’): ein Obazda, der Obazde, des Obazden, mit Obazdem, den Obazden to randomly jump through a few different cases.