What has been called "liturgical drama" is just a name for (parts of) church offices. Some of them, like the Palm Sunday procession were always "outdoors" events. Some of them, like the Mandatum, are "indoors" even today. On the other hand fully fledged Passion plays were staged in churches by the Jesuits and Piarists in the 16th-18th centuries. But there actually were ceremonies which were part of the liturgy and were being banished at different times from different churches, if necessary. It was the Feast of Innocents with the famous Boy Bishop as celebrant. Like in the joke about getting rid of smoking, every bishop could have said: Banishing theater from the church? It is very simple, I did it many times!
    Here I want to discuss two things.
    (1) Let me recall first a nice specimen of "liturgical drama" - different from the famous Quem quaeritis : without dialogue, but with excellent dramatic action. It is quoted from Young (vol. 1, p. 107-8:

Post Primam quidam sacerdos dicit Missam Episcopelli ad altare Sancte Crucis, et ibi a dextro latere altris preparatus est Episcopellus cum pluuiali et mitra, et cum capellanis suis. Officium Ex ore infantium. Epistola Vidi supra montem Syon.
    Quam dicit quidam indutus quadam uili | stricta, et tenet in manu quandam hastam ligneam, quam prohicit uersus populum. Et ibi sunt quidam armati, qui secuntur dictam hastam, et circuiunt ecclesiam querendo Infantem cum Matre sua, scilicet Christum cum Beata Uirgine (108) Maria. Et est quidam indutus ad modum mulieris que sedet supra Asinam fugientem per ecclesiam, ad significationem Uirginis fugientis cum puero Egypto secundum quod angelus Domini in sompnis dixerat Ioseph.

(2) My second point is the oldest prohibition of "theater" in the church (I know of), ordained by Innocent III in 1207 and concerning the head of the Polish church at the time, the archbishop Henryk Kietlicz of the capital Gniezno. (For the full text see ** at the bottom of this mail. In my new book, in progress, I am preparing a discussion of this document). The decree is pointing at corruption of the church caused by married canons: if they unwisely allow their sons to the offices, soon public games are being held in those churches; not only monsters in masques are introduced, but on three annual feasts following Christmas [Innocents, Circumsision and Epiphany], diacons, priests and subdiacons subsequently, showing their madness, are corrupting the people:

...per insolentiam eorundem interdum ludi fiunt in eisdem ecclesiis theatrales, et non solum ad ludibriorum spectacula introducuntur in eas monstra larvarum, verum etiam in tribus anni festivitatibus que continue Natalem Christi sequuntur, diaconi, presbyteri ac subdiaconi vicissim insanie sue ludibria exercentes, per gesticulationum suarum debacchationes obscenas in conspectu populi decus faciunt clericale vilescere...

With best regards,
 

Dr Andrzej Dabrówka
Polish Academy of Sciences
Institute of Literary Research
http://www.medianet.pl/~dab/and/teatr.htm
http://www.medianet.pl/~dab/and/

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*My book I am referring to - THEATRE AND THE SACRED IN THE MIDDLE AGES (2001);
has got an English summary: "http://www.medianet.pl/~dab/and/tis-e.htm"
____
**
Innocentius Pp III, 1207 Jan. 8, interdicit archiepiscopo Gneznensi et suffraganeis eius, ne publice uxoratos admittant ad ecclesiasticas dignitates, simulque mandat, ludibria publica in ecclesiis extirpent.
                 [Inc.] Cum decorem domus Domini et locum tabernaculi glorie sue diligere vos oporteat, accurata vobis est sillicitudine precavendum, ne in commissis vobis ecclesiis illatempere presumantur, que vel in eis lampadem religionis extinguere, vel munditiam videantur ministrorum domini maculare. Ad nostram siquidem noveritis audientiam pervenisse, quod quidam in vestris diocesibus constituti, publice cum mulieribus contrahentes ecclesiasticas non verentur suscipere dignitates, et nonnullarum ecclesiarum canonici, quorum lumbos iuxta verbum evangelice veritatis deceret esse precinctos ac in eorum manibus lucernas bone operationis ardere, usque adeo luxurie sordibus putruerunt, quod nec etiam ignominiam suam velint turpitudinemque velare, quin se reddunt indignos, indignius secum trahunt; ac si non satis in opprobrium ordinis clericalis eorum incontinentia foret cognita, nisi natorum, in  publicum deductorum loquentiumque testimonium, contra ipsos esset ostensione sedula comprobata. Cumque in ecclesiis in quibus huiusmodi clerici locum habent multa enormiter attententur, dum in eisdem fermentata patrum et filiorum, nepotum etiam et affinium parentela inordinate ministrat, quia videlicet amore predominante carnali reverentia spiritualis tepuit inter ipsos, unde nequaquam unus quodlibet facere propter alium pretermittit: per insolentiam eorundem interdum ludi fiunt in eisdem ecclesiis theatrales, et non solum ad ludibriorum spectacula introducuntur in eas monstra larvarum, verum etiam in tribus anni festivitatibus que continue Natalem Christi sequuntur, diaconi, presbyteri ac subdiaconi vicissim insanie sue ludibria exercentes, per gesticulationum suarum debacchationes obscenas in conspectu populi decus faciunt clericale vilescere, quem potius illo tempore verbi Dei deberent predicatione mulcere. Quia igitur ex officio nobis iniuncto zelus domus Dei nos comedit et opprobria  exprobantium ei super nos cadere dignoscuntur, fraternitati vestre per apostolica scripta mandamus, quatenus, ne per huiusmodi turpitudinem Ecclesie inquinetur honestas, eos  qui sunt publice uxorati non admittatis de cetero ad ecclesiasticas dignitates, et admissos repellatis ab eis quas non possunt sine pravo exemplo et gravi scandalo retinere. Filiis quoque canonicorum, prebendas in eisdem conferri ecclesiis non sinatis quarum sunt canonici patres eorum: cum indecorum sit, ut in altaris officio illegitimus filius impudico patri ministret, in quo unigenitus Filius  eterno Patri pro salute humani generis victimatur. Prelibatam vero ludibriorum consuetudinem vel potius corruptelam, curetis ab ecclesiis vestris taliter extirpare, quod vos divini cultus et sacri comprobetis ordinis zelatores.
[quoted from the Kodeks Dyplomatyczny Wielkopolski, vol. 1, No. 55, pp. 57-580;
its source was: Breguigny et du Theil, Diplomata, chartae etc. II, p. 1037].