I don't know what church you're referring to or the circumstances under which talking about depression would take place. How do we know it is not taboo as things already are the way they are in many churches? What is not said in the pulpit on Sunday may well be said in less public situations.
Other than that, however, while I certainly don't think the subject of depression should be taboo anywhere; I really think our whole culture could do with a little less talking about mental illness and a little more learning, exactly, the difference between being all "happy-pappy" and at peace with the world and all that's in it all the time; and the very normal state of not being "all happy-pappy-all-the-time".
So, in general, I think if someone thinks s/he may be depressed s/he should go seek professional help (and if that person starts looking for help first with clergy then I'd hope the clergy-person recommended the same thing. Other than that, there is, I think, a vast, vast, and widespread degree of overzealous ignorance about, and enthusiasm over, the subject of mental illness; because a) many people aren't "happy-pappy" all the time, and b) "cheap" and "lightened up" information about mental illness is so pervasive in our culture it is posing serious danger to people in a number of different ways (whether that's the perfectly normal person who isn't entirely happy at the moment, or whether it's strangers, friends, family members who keep an eye out on who/what they - in all their "infinite lack of wisdom and information" - think might be one or another type of mental illness in someone else.
Personally, I have no problem with any church that sticks to matters of faith/belief and leaves the mental-health/health stuff to the mental-health/health professionals. Of course, I'm a big one for believing that all things in/aspects of life should be neatly separated into their own "category"/"department", with clean/clear lines preventing "everything and everyone" from turning into one, big, blob, of a mixed up and unsorted mess with everyone/everything putting in their two-cents and/or spin on it all.
I suppose the appearance of "taboo" could exist if "the church" (whoever/whatever that is) is particularly cautious about calling all unhappiness, "depression" and seeing it as a mental illness. Then again, I think of a very religious/devout woman (not clergy) at my father's wake and how she had the nerve to tell me I should be "joyous" and not sad (????? !!!)