We will paint a picture, based on sources, that is somewhere between “clear halacha” and “personal preference.”
The Rama[2] cites an opinion[3] that people should stand[4] throughout chazarat hashatz. On the one hand, he presents it as an opinion; on the other hand, he does not mention those who disagree. The implication is that this is something people are expected to do, but it is not clear that it is a categorical requirement, like standing during Shemoneh Esrei itself. The Mishna Berura[5] explains that since listening to the shaliach tzibbur[6] is considered like speaking (shome’ah k’oneh), it is as if one were reciting Shemoneh Esrei himself, and one should therefore stand. Extending the logic further, it might follow that one must keep his feet together during chazarat hashatz, but the major poskim do not mention this, and very few people have this practice. Indeed, many sources indicate that chazarat hashatz is different from Shemoneh Esrei.
The Rambam[7] writes that during chazarat hashatz “all are standing (omdim) and listening,” which seems to imply that one should stand. However, some[8] poskim point out that since the Rama did not name the Rambam as his source, it is possible that the Rambam is referring not to the position of the body, but rather to the stopping of activity.
Although the views of poskim vary, the primary thrust of the consensus is as follows. The historically normative, preferred practice is to stand during chazarat hashatz unless there is good reason not to. Clearly, however, there were times and places at which very respectable people and communities did not stand. Furthermore, the matter should not be viewed as an outright obligation.[9]
Indeed, in some cases, the straightforward advice would be not to stand. If one is weak or sick, he can feel free to sit during chazarat hashatz. (This is true even when he can find the strength to stand for Shemoneh Esrei itself.)[10] If standing encourages people to roam around and thereby detracts from their own and/or others’ ability to concentrate on chazarat hashatz, it is better that they sit and follow in a focused manner.[11]
The case you speak of, a congregation in which a clear majority sits, is a tricky situation and appears to involve two related concepts. One is yohara (haughtiness). Classic yohara is when one does something that is a clear stringency in a context that can be construed as haughtiness. Is standing an act of yohara, and thus undesirable? Despite the general lack of adherence to the halachic preference for standing, it is difficult to consider that one who stands in accordance with the instructions of the Rama and many others should be placed in that category. The other relevant concept is al yeshaneh mipnei hamachloket (do not act differently from others because it can cause conflict). The gemara applies this idea not only to cases in which someone is more lenient than his peers, but also sometimes even to someone who is stricter than his peers.[12] In a shul in which only a few people stand and it is the type of community that is (overly?) sensitive to matters of possible yohara, we would discourage people from standing and thereby standing out.
It is important to note that even if one sits during chazarat hashatz, he should wait to do so until after the beracha of HaKel HaKadosh, following Kedusha, and he should stand during Modim D’Rabbanan, due to the bowing done at that time.[13]