I agree that ignoring people is a good idea...if what they are saying is off topic and personally attacking. On the other hand, I do believe it's unwise to ignore somebody who has a strong point of view and expresses it without personal attacks and/or getting off topic.
On the other hand, maybe you don't wish to actually discuss some things and when you do, want people to just agree with you. That would be nice, wouldn't it? Unfortunately, people do disagree and sometimes the "other side" is irritating not because they display any personal animosity or fall into the two most prevalent logical fallacies (ad hominem and ad populum) but because they just have strong arguments and the arguments you are using are either not persuasive to them, or not generally persuasive to many. In those cases, you either continue the discussion or you exit it. My recommendation would be to exit the discussion, not the person. For two reasons.
First, exiting the discussion removes the irritation. If you can't persuade your "opponent" and he/she is using responding reasonably civilly, I would suggest you don't know the subject well enough and ought to either leave the discussion or do some more sophisticated thinking about it so you can meet his/her points civilly and confidently, and with better arguments. If you feel strongly about the topic, it's just respectful to work on and bring your "A Game," as they say.
Second, it may be you need to exit the thread/subject. Fine, no point in building up steam needlessly. But leaving the topic doesn't mean you have to ignore every other thing that person says. It's like a good meal at a fine restaurant. You don't like the peas? Don't eat them. But don't throw the steak out just because you don't like the peas. In the end, few posters are so completely obnoxious and mean they should be completely ignored.
As one who has, I believe though I don't know for certain, irritated enough players with one particular topic I argue strongly about, and been placed on their "ignore" list, I have always thought it would have been better for them and myself to have had them leave the subject rather than ignoring everything I say. I do have a reasonable number of people who are "following" me and thus, I believe, I may have something to say from time to time. I mean, accidents do happen, right?
In the end then, the point is that if you are irritated because of incivility across a wide range of topics, ignoring may be the best bet. But if you are irritated because they have a strong opinion my recommendation is you just ignore that topic and keep the relationship.
AJ