How do you draw the line between being a good ideologue and a bad one?

We all need some guiding principles that we hold dear. Without any, a citizen of a free nation would see nothing wrong with abandoning their freedoms in favor of a new Enabling Act allowing some latter day Hitler to grab the wheel and steer the ship of state into genocide and destruction. But we have to be vigilant not to become too ideologically ingrained, to the point we reject perfectly logical and even necessary political policy proposals because they run afoul of a cherished belief system we are unwilling to hold up to critical analysis.

How do you decide where to draw the line. And once you have thought this through, and know that on most issues, you are open to fresh ideas and willing to question your beliefs in light of new evidence, how do you deal with true ideologues who debate along the lines of:

X is true. I say it’s true. Nothing you do can convince me otherwise. If you don’t believe in X you have a closed mind. I like it at least. It’s true. Oh, shut up and have an open mind! Of course it’s true!! Of course, “Oh shut up!” is generally stated in far cruder, more emphatic language. And the sheer comedy of this is their utter refusal to look at conflicting facts while simultaneously insisting that it is anyone who doesn’t share their ideology who is prejudiced. It matters not a whit if you are open to new ideas. Is there any way to prevail against such a debater?