You might note that, in the posts on tradition, I have so far kept things very general, following the dictionary definition of "tradition" as a kind of "pattern of thought, action, or behavior." I haven't written anything specific to religion, much less to Christianity, yet.
This approach of saying as much as I can before bringing religion into it is something I've used before, notably in the warmly received "Graph Theology of Faith" series of posts from this past Christmastide. It's not an original approach, of course, but I think it offers certain benefits that repay the effort of not jumping the gun. Let me suggest three of them.
One benefit to discussing what can be discussed without reference to religion is that it delays the inevitable religious disagreements. There are certain aspects of certain topics that a Catholic and a Calvinist are simply going to disagree on, and the longer they stay away from these aspects the more they may find aspects they do agree on. The experience of agreement -- by which the parties learn that they can learn from each other -- may make the eventual disagreement a better experience for all.
Another, related benefit is that it may reveal disagreements that are usually expressed in religious terms but turn out to have a more general basis. Two Christians may find that their doctrinal differences arise from their philosophical differences, and see that debating doctrinal conclusions directly will be fruitless, since they accept mutually incompatible philosophical premises. An atheist may discover there's more to refuting a Christian than flat rejection of his appeal to authority; the appeal may be very different for the two because, say, they have very different ideas about what human knowledge really is.
Finally, I think putting off the religious aspects of a question as long as possible helps broaden the thinking of the one who does it. With tradition, for example, you can explore questions without immediately placing them into the stock contemporary positions. Reject a tradition from your patrimony? You contemptible heretic. Not look to import a tradition? You hidebound blockhead.
In other words, it forces you to think of the subject in general human terms, not specific political terms. That, in turn, can help you understand general human nature in a way you wouldn't have considered if you started with a specifically religious context. (E.g., what are the similarities and differences between my faith in my friend and my faith in my God?) And that can help you understand how the Faith relates to all human experiences.
[None of this is to suggest that what we say outside of an explicitly religious context is unaffected by our faith. There's almost nothing I can say about anthropology, for example, that isn't ultimately grounded in what the Faith says man is, and my confidence in making the bold statement Brandon noticed in the previous post also comes from faith. But the above benefits may still obtain in such cases.]