Well to be fair you also have to realize who the liberal person is one each end. The liberal person on American Dad is Hayley, the daughter character. Who has constantly been shown to out of everyone in the family (even more so then Klaus of all people) to be the one ignored out of any development or general screentime. In fact in the latest slew of eps anytime she's on screen the joke is that she is being ignored and... that's it. Move on to someone else.
Brian is one of the cornerstones of Family Guy. Not only due to being voiced by MacFarlane but also to being one of the most deep and evolved of the main cast besides Stewie. And since the two work too well together they can never just ignore Brian. Also it's not like he isn't ever made fun of or knocked around (episodes like "Brian Goes to College" and "We Love You Conrad" seem to just make that the point of the ep actually) and even his liberal views sometimes get mocked (like in "Road To The Multiverse").
You also have to remember that American Dad when it was first being concepted was around the time that Family Guy was cancelled and it didn't look like it was coming back. Thus it was made to be Family Guy's replacement with some differences. When FG came back they could make American Dad into something else and I guess decided FG would be a better place to push the whole liberian message especially since FG is the more popular show. I do grant you that it is quite ironic but there is reasoning behind it.