I got an honorable discharge, but I have heard it is possible for people to get an "other than honorable discharge" upgraded to an honorable discharge after a period of time. Not sure exactly how that works.

If you get a dishonorable or other than honorable discharge, it might make it more difficult to get government jobs, but I think most non-government jobs wouldn't give a shit about your discharge status as long as you didn't do something crazy. Refusing to take part in a political photo op in DC would likely help you with conservative employers anyways.