Not every Shevus pushes aside Shabbos, as is evident from the Sugya in Pesachim (65b, 66a) where Haza'ah not pushing aside Shabbos is discussed (although there is an opinion there that it does push aside Shabbos) as an example of one of the Shevusim that Chazal decided does not push aside Shabbos. Moreover, the Rabbanan decided it should not be done even if it will cause someone not to bring a Korban Pesach, as stated in Pesachim there.

One possible reason that Chazal said it does not push aside is because it usually can be done before Shabbos if one starts getting sprinkled earlier (i.e. makes sure he does not have to be sprinkled on the third or seventh day). Even when he has no choice or else he will miss doing a Mitzvah (i.e. Korban Pesach), the Rabbanan decided it is worth it to uphold that people should not generally do this Shevus on Shabbos.

All the best,

Yaakov Montrose