Sure you can. Government needs great, enthusiastic people working at every level. Some people see it still as very straight laced and some of it is, but there are some offices where they don't care what you look like. It is like anything else in the world, you just have to find the right people/place. There are strict discrimination laws, so if you have your hair style for religion then you can't be discriminated against because of that. I've worked at various levels of the government from local city, to state, to federal and have seen all sorts of hairstyles, clothes, etc. Currently I work in an office that is more conservative, so things that I wore in my previous office don't work here. Each office and job will be unique, so some will really care if you deal with the public and some won't. If you are in a more liberal location and work for the city they might not care at all. I would always just ask if there is a dress code and hair styles will normally be part of that.