NewChapter - "I am disturbed that the society was touched by a political/religious authoritarian movement."
It's never been actually documented; it's more something I personally deduced after learning about the Christian Right's origins and some of the eerie similarities in their interpretation of Biblical prophecy; it seemed like WT eschatology, but militarized. Once I realized it, I wasn't surprised, though; the WTS has had a history of occasionally playing ball with "worldy" political entities when it suited them; until recently, it simply had more success keeping it on the down-low. In another life, Rutherford would have been as Right-Wing as Father Charles Coughlin.
Political neutrality was the WTS's official position, but Rutherford was so obviously a hard-core Social Dominator (arguably even a Double-High), that his stance was probably solidified in response to the Nazi movement in Germany pre-WWII. Rutherford had originally extended an olive branch to the Nazi leadership in the form of a somewhat antisemitic letter; my guess is the Nazis percieved (correctly or otherwise) what might otherwise be kindred spirits in Rutherford and his followers, but were smart enough to realize that rather than allowing themselves to be assimilated under the European fascist umbrella, the WTS (as an extremely successful authoritarian group in the US at the time) would, in the end, be in competition with them.
In addition, polls have pretty clearly and consistantly demonstrated that the vast majority of the JW R&F (in the US, at least), while not actively voting/political, hold personal social and cultural views that identify far more with the Right-Wing than otherwise (with one or two exceptions).
As the vast majority of authoritarian follower-types con't help but be heirarchal in nature, and thusly naturally tend to defer to some kind of authority figure, I suspect Rutherford (correctly) intuited that political "neutrality", by default, would result in a "vote" for him.
NewChapter - "Even in the org, I tended to be liberal minded."
Same here; and I used to tell myself that, at heart, the WTS was really a progressive organization, and that it's positions on evolution, homosexuality,transfusions, etc., would inevitably go the way of the dodo, until I realized that if they did, the WTS would have to literally rewrite huge swaths of their theology; in effect, overhaul the entire religion and start from scratch (as the late GB1.0 member Dan Sydlik allegedly confessed in private once).
A conservative/authoritarian organization, however, simply cannot do that; it's operational structure is virtually engineered to prevent it from happening. Any substantial progressive reform at this point, and they would arguably no longer be Jehovah's Witnesses.
NewChapter - "I've noticed that some people leave that org only to hook up with another authoritarian group."
A few, yeah; they seem to need that kind of structure in their lives. For me, the WTS did such a thorough job discrediting other forms of religious expression, that at this point in my life, I can't see myself joining any religious organization (although when my fade first started, I was leaning a bit towards Unitarian Universalism). My family and I seem to be managing fine without it; in fact, I'm mostly agnostic at this point (and yes, I realize that UU happily accepts agnostics, but the whole "lighting candles and holding hands while singing" is just a bit too ritual-ish for my taste; I find the open-forum philosophical/theological roundtable-type discussion appealling, though).