How is it a substantial change to the theology of the mass [for the congregation] to say responses with the servers, or to recite something that the people sing at a sung mass?
In doing figuratively what postconciliar architecture did materially—dispense with the altar rail—congregational participation (i.e., dialogue mass) effectively nullifies the hieratic dimension of the liturgy and replaces it with the theological equivalent of a parliamentary session or, less grandly, a politician's press conference. To continue the analogy, in both liturgical forms someone is in the chair, true enough, but in the latter the shouts from the gallery or the hall are no longer disturbances but are instead an integral component of the process.
What is more, there is simply no honest or authentic sense in which congregational participation can be argued or understood to be a mere reclaiming of the participatory function nominally ceded to the server in the historico-liturgical development of the Mass. It is hardly coincidental or immaterial or inconsequential that, right up to the conciliar revolution, the server, in his capacity as stand-in for the congregation, was rubrically required to be a man in orders, at least normatively. To shift, if I may, from the general to the particular, even when I became an altar boy, less than ten years before the opening of the council in October 1962, my contemporaries and I were taught that our presence on the altar was a great privilege rooted in a dispensation that was itself rooted in necessity. Thus, the two steps—the first (from a man in Holy Orders to an indulted lay man or boy) and the second (from an indulted server to a chattering mob covered hastily with the intellectually desperate fig leaf of the "priesthood of the laity")—are scarcely comparable in height!
My recollection of the Latin mass is the priest doesn't say the responses the servers say.
And the people sing the creed at a sung mass. Does that take away from the priest?
At a Traditional Latin mass celebrated by an unaccompanied priest, he does indeed make all the responses. As for a sung mass, the theological parallels between the choir and the server have been almost entirely forgotten (or perhaps willfully expunged), even by Trads. Before the twentieth century, those who sang in any liturgical setting were expected either to be in orders (tenors, basses) or to have the potential to be in orders (boy sopranos and altos). As with servers, here too the presence of laymen was a consequence of dispensation or indult—although admittedly of great antiquity, as at least in England and France there were, to my knowledge, large lay cathedral choirs as long ago as the fifteenth century and perhaps much earlier.
Still, whatever the practice and however long its existence, the central point that has been either forgotten or memory-holed should be rescued from oblivion: in Traditional Catholic liturgical theology, choirs, like servers, assist materially in the celebration of Mass and thus are normatively expected to be in orders. The "assistance" that the congregation is said to offer at Mass is precisely that: something that may be compared with what is done by men in orders only in the very limited special-use sense that the quotation marks signal.