If You Disagree So Much, Why Are You Here?
The first thing to note is that it's an argument about the opponent's substantive views, and hence different from accusations of trolling or disrespectful presentation (though the same commenter may face both sorts of accusations from different people). It says that a certain level of disagreement on the issues is enough that you have neither justification nor concievable motivation to continue reading and commenting.
With special interest blogs, that kind of argument makes sense. There really is no good reason for a person to go on, say, a knitting blog and post repeatedly (even if completely sincerely) that knitting is boring and the blogger ought to go buy their sweaters at Wal-Mart like a normal person. With political blogs -- those that advocate for or against changes in public policy and culture -- it's different. Knitting can be practiced privately by knitters, and it doesn't affect anyone else. But political issues affect everyone in a given society. Liberals and conservatives can't just go off to their own clubs and leave each other alone (like, say, Trekkies and Star Wars fans can), because the two groups have to share the same tax rates, the same prevailing attitudes toward sexual harassment, the same air quality, etc.
The fact that political discussion is about issues that affect everyone, not just those who agree with the policy in place, means that there's a basis for cross-ideological discussion. A person can justifiably seek out engagement with opponents -- even those with very fundamental disagreements -- for a variety of reasons: to evangelize, most obviously, but also just to understand the other side, and even perhaps to learn something from them and discover that they're correct in some way.
There are, at the same time, good reasons to avoid cross-ideological engagement: to strategize with fellow-travelers, to work out intra-factional disagreements without the distraction of having to justify everything from first principles, or to have a respite from cross-ideological engagement elsewhere. It's entirely reasonable for a blog author to declare that the purposes of their blog are best achieved by limiting certain cross-ideological engagement -- e.g. "this is a blog for environmentalists to talk about how to address climate change, so we're not interested in arguing about whether climate change is real or not." (Or even "this is a blog for us to have fun mocking climate change deniers, so we're not interested in substantive arguments about whether climate change is real.")
The argument in this post's title assumes that the obvious default -- or even the only reasonable course of action -- is to limit cross-ideological engagement. I think this is wrong, and in fact I would argue that for a publicly-posted blog, the default is to be open to cross-ideological engagement. The blog author can limit that engagement to any degree they want, but it requires an affirmative declaration. Once such a declaration is made, the proper response to ideological opponents is "this isn't the place to discuss foundational disagreements like that," not "why are you here if you disagree?"
It should be said that the titular argument often arises out of a reasonable frustration on the part of the blog author and their fellow travelers. I know I've thought it about several commenters who seem to pop up in every post by Hugo Schwyzer to accuse him of being misandrist and having double standards. Their arguments seem to be making no progress, so I begin to wonder why they are there. But I have to remind myself that they have every right to try to engage in cross-ideological debate unless and until Schwyzer declares that his blog is not the place for debating the foundations of feminism (and I should note too that as fruitless as his commenters' quests seem, Schwyzer doesn't seem to be making any more progress in winning them over to his side).