My claim is that a member of the secular left is ill equipped to respond to bad religious arguments of the religious right (and, by the way, knowing whether the religious conservative is operating from fundamentalist premises can be important).That is a statement with which I would agree, but I'm not sure how much the understanding of bad religious arguments would make for a member of the secular left. For one, religious arguments hold no sway for members of the secular left, and it does us no good to counter religious arguments with further religious arguments. In this sense, it is the mainstream Christian right's and religious left's lack of understanding of bad religious arguments from the religious right that can be, and is problematic, because many mainstream conservative Christians will be convinced by these, and many liberal Christians will be unable to counter them on the basis of common theological ground.
Where the real problem of lack of understanding on the part of the secular left lies is in our general tendency to lump all religious members of the right together, a point that Shiffrin also makes. The religious right is a small but vocal minority within the political right, but the right as a whole is overwhelmingly Christian. Lumping the religious right and more main stream conservative Christians together causes us to fail to understand the often subtle differences in their positions and arguments which, while the theological soundness of those arguments is irrelevant, can make it difficult for us to address them from our own perspectives.
But this problem is overshadowed, from the perspective of the religious left, by the almost complete lack of understanding of the our world-view by Christians on both the left and right. It is virtually impossible to find a veridical characterization of the secular left from anywhere on the right. The secular left world-view is treated by the right as a form "postmodernism" which to most on the right is a synonym for "relativism." Yet for the most part, members of the secular left hold values that they consider objective, or at least absolute, such as tolerance and the avoidance of cruelty. Very few of us are relativists, and even those of us who are do not adhere to the caricatured form of relativism, in which all values are entirely subjective or culturally dependent. Our objective values are the basis for our arguments against common religious positions such on issues like choice, affirmative action, gay and women's rights, and the environment. The right's, and even the religious left's failure to grasp this makes communication damn near impossible. Their representations of our positions and arguments will be entirely mistaken, so long as they do not include the fact that the values from which our positions are derived are not merely blowing in the wind like so many dandelion seeds which may be carried away at any moment.
One of the reasons I like George Lakoff's political writings (and you know it has to be a good reason, given how much I despise his cognitive science) is that, however much he gets the actual substance of the secular left's value-beliefs wrong, he goes out of his way to emphasize that the positions of the secular left are value-based, and that those values are stable parts of our world-views, rooted in our interpretation of the empirical world. One would be hard pressed to find a characterization of the secular left that is consistent with this from anyone on the right, and especially from the religious right (one could read any post from Joe Carter on secularism to see how badly the religious right gets the secular left wrong). This is, I think, one of the most pressing problems for the secular left, and its importance for our influence on the general political discourse in this country far exceeds that of our lack of understanding of the nuances of Christianity on the right. Until the right is able to develop even a rudimentary understanding of where we are coming from, we will be unable to communicate with them effectively, and, as both Lindsay and Lakoff point out, if we are able to communicate with them at all, it will have to be on their ground.