There is an interesting explanation to the question as to why we do not blow the Shofar if Rosh Hashana falls on Shabbat. The same question applies to why we do not take our Lulav on Shabbat of Succot.
The difficult part of the question is that both Shofar and Lulav are Torah laws, and yet the rabbinic concern that we might come to carry, outweighs these Torah laws.
The answer to this question has to do with the concepts of קום ועשה, "Get up and do it", which applies to positive commandments, and שב ואל תעשה, "Sit and don't do it" that applies to negative commandments.
The Mitzvot of Shofar and Lulav are positive commandments. If we fulfill them, we have fulfilled the Mitzva. If we don't do the Mitzva, we haven't done anything wrong. In this case, we are commanded to שב ואל תעשה, stay at home and do not do the Mitzva.
The Rabbis felt that the risk of carrying had more at stake than Shofar and Lulav. Carrying on Shabbat could be punishable with סקילה, stoning. Therefore, better not to fulfill Shofar and Lulav, that is not a sin, but an unfulfilled Mitzva, than risk carrying that is a very severe negative commandment.