A famous musicologist, writing in 1947 about the Bach cantatas, tells us that there is no word from the seventeenth or eighteenth century to say whether or not the congregation joined in the concluding chorales, and modern critics cannot come to agreement on the matter. If the congregation did join in, they must have been confused when, as not infrequently happened, Bach chose to set the chorale in a fantasia construction. Moreover, a simple chorale occasionally appeared in the body of a cantata.

Our question is, has word now finally come through from the seventeenth or eighteenth century? One would think that there must be some reference to the practice somewhere. Can any Member aid us in our nescience?

I think the very reasons Sydney suggests are among the reasons it's now thought extremely unlikely to impossible that the congregation would have joined in. Or at least that Bach would have intended them to. The congregation may well have sung chorales, perhaps supported by whoever wasn't singing in the cantata at that service (he only used one voice per part in the cantatas the vast majority of the time) but if they did it wasn't in Bach's cantatas but elsewhere in the service. Of course the chorale melody would have been an old friend for them to recognise in the middle of Bach's music in any case.

Besides the fact that Bach often had little instrumental bits between the chorale lines in his concluding settings (think of the last chorales in parts 1, 4 and 6 of the Christmas Oratorio) sometimes there are also slight variants even in the melodies which are set 'simply' and the congregation wouldn't have known they were coming.

The keys chosen are also not always the most friendly for congregational singing. Wachet auf goes up to a G. Ever heard a congregation try and give that note a go?

What to me seems the best-informed contribution from that site begins like this:

Doug Cowling wrote (March 16, 2005):
[To Boyd Pehrson] I think the case against congregational participation rests on two arguments.

The first is that the cantata, like the organ prelude, is not an integral part of the Lutheran mass but a glorious adornment. What I mean by "integral" is that it was not a mandated item in the liturgical ordo.

A worshipper arriving on an ordinary Sunday at St. Thomas' expected to sing six chorales: before the Gospel (de tempore), the Creed, after the Sermon, before the Sanctus, during the Communion and after the Benediction.

They expected the choir to sing the Ordinary of the mass -- Kyrie, Gloria, Sanctus, etc -- either in motet or concerted style. In parishes without a choral tradition, the people would have sung the metrical paraphrases of the "German Mass" (e,g. "Allein Gott in der Höhe" for the Gloria). This is the brilliant provision which Luther formulated, a solution to encourage music where there was no endowed choir school.

Wealthier members of the parish may have bought a libretto with the cantata text, but the vast majority of people in the pews would have had no idea what music was about to emerge from the choir loft. There wasn't even a standard form to the cantatas: they didn't all end with a chorale. And even when they did, there was never more than one verse. A congregational chorale was more likely to have a dozen verses.

Unlike the predictable occurrence of the chorales listed above, a chorale could occur anywhere in a cantata. I'm sure this list could point out examples of chorales in just about every imaginable sequence.

There's more but you can easily find it by searching the page for the date of Cowling's contribution. I don't think David Glenn Lebut Jr.'s arguments have any substance, strident though they be.