Provide at least your system info when you ask for help so people know your hardware at minimum.
Also what version of Proton are you using in Steam Settings (or in the game properties if you set specific Proton per game)?
Did you try to disable/enable esync or fsync?
According to ProtonDB the game seems to work.
Here is a Steam guide for the game on Proton, not sure info is relevant or up to date [GUIDE/STATUS] Bannerlord on Linux w/ Proton :: Mount & Blade II: Bannerlord [EN] General Discussions
Check the game log for the crashes and why they occur.