Some other posters recommended single rooms. However, those are rather uncommon at the Berkeley dorms.
The odds are in favor of a “random” roommate being fine, but that still leaves the possibility of a problem roommate through luck of the draw. The dorms do have a Unity Theme house or section described at http://reslife.berkeley.edu/academics/theme-programs/unity-house-theme-program which presumably reduces the risk of a roommate who could be a problem in this respect (note that it comes with academic requirements).
Other housing options include the BSC co-ops, which are very low cost, but can have long waiting lists (apply as soon as possible if interested). However, the theme houses (including Wilde whose theme is LGBTQIA & Queer) may be easier to get into, and the co-ops in general tend to attract more left-leaning students anyway. See https://www.bsc.coop/index.php/housing/houses .