To feel contempt and bite your tongue, now that is a hard thing to do. Some people probably feel that you shouldn't even attempt such a thing. After all, wouldn't that be betraying your beliefs? Or showing that you are too weak to stand up for what you think is right?
Or would that instead be civility? Perhaps grace? Hmmm..
I'll tell you what I think. We have filters between our thoughts and our words for a reason. It's important to recognize that highly charged emotions remove those filters. Since it means you have lost an important social convention, feeling a strong emotional reaction to something is usually a good indication to hold your tongue. If you don't, you probably will not shine the best light on yourself.
It takes restraint, but to have that restraint is to have grace. Grace, civility, forbearance- these are virtuous qualities, I think most people would agree with that.
Difference of opinion is great. Honest debate leads to better understanding. On the other hand, contemptuous bickering between two sides deeply set in their beliefs is neither productive nor instructive. The annoying thing is it only takes one person in a group to turn the former into the latter.
Differing opinions exist not because of ignorance, but variances in perspective. Seeing something from many angles is extremely helpful in understanding that thing, whatever it is. It isn't helping anybody to drive people with a certain vantage point out, especially when that viewpoint is from an angle many of us would like to see things from one day. Assuming ignorance drives dissenting opinion is, well, ignorant. The person you disagree with probably understands your stance perfectly, they just see things differently than you, and that isn't necessarily a bad thing.
The short version- my advice is if you have a strongly negative emotional response to something anybody says, go ahead and type your post up, let it all out... then, instead of posting it, just delete it. Everybody, including you, will be better off for it.