I know this is an old topic, but I thought I’d add our experiences of running a forum that’s now in its 19th year and has tens of thousands of members.
Three main things come to mind:
1. Keep political discussion corralled.
We consider it important to ensure that political discussion doesn’t spoil the enjoyment of what our members are mostly there for, so we keep it corralled in a specific “Politics” category and don’t allow it to spill out. The guys who are interested in talking politics know where to go, and the ones who aren’t know they can avoid it.
2. Keep it under your thumb.
We’re clear in our guidelines about what is not acceptable (hate speech, personal attacks, name calling etc) and we don’t wait for people to flag problems to us. We proactively monitor the Politics category and step in when necessary.
3. Have clear sanctions - and apply them.
We don’t want to boot people off the forum; we want them to change their behaviour when it drifts out of line. To that end, we have a clear four-step system of sanctions that are detailed in the guidelines:
- First warning: The member is told what he has done that’s not acceptable and warned that he may lose the right to post in the forum, temporarily or permanently, if that behaviour continues.
- Temporary suspension: If the behaviour is repeated a second time, the member is suspended for two weeks. Suspending (rather than silencing) the user means he can’t even log in, so he can’t keep up with topics during this period.
- Final warning: If the member displays the same behaviour on his return to the forum, he gets one last warning and is told clearly that this is his last chance - he’ll permanently lose the right to post in the forum with no further warning if this behaviour continues.
- Permanent silencing: If he does not change his behaviour after being given every opportunity to do so, he is silenced. This is not revoked, under any circumstances.
As well as being sent directly to the member, all notifications of these sanctions (both warnings and exclusions) are posted publicly in the topic(s) where the problematic behaviour was displayed. They are posted as replies to the posts that led to the sanction and they quote the specific offending content, so everyone can see clearly what, why and who.
Every single member who gets excluded accuses me of bias, so apparently I’m biased in favour of both liberals and conservatives 
but I frequently receive messages from other members praising my even-handedness. I think the transparency is key to that, as @Heather_Dudley has stressed.
When we put these clear sanctions in place, it was a case of ‘shape up or ship out’. We ended up permanently excluding very few of the previously problematic members; the vast majority did change their behaviour in order to be able to stay. The problems now mainly come from new members who arrive in the Politics category shooting their mouths off because they’re unaware of the guidelines. I point them in the right direction and gently give them the ‘shape up or ship out’ message.
Frankly, the Politics category most certainly takes over 90% of my time and energy as moderator. We considered simply banning political discussion altogether, but my view is that I’d end up playing whack-a-mole with political posts and topics being started in other categories. Better to keep it corralled and keep it under my thumb, so it doesn’t spoil the fun in the rest of the forum.