it will be the only place in the entire Jewish world that a shofar will be blown
Twaddle!
I used to belong to a synagogue where the shofar was always sounded on the first day of Rosh Hashanna.
The Torah says: "On the first day of the seventh month hold a sacred assembly and do no regular work. It is a day for you to sound the trumpets." (Num 29:1)
It doesn't say, "except if it's Shabbat." IMHO, it is against Torah Law NOT to blow the shofar on the first day of the seventh month, i.e. Rosh Hashanna. The prohibition arises from a Rabinnic prohibition against carrying things on Shabbat. And even with this, the prohibition doesn't make sense as the shofar blower could leave his shofar at the synagogue before Shabbat. Following the logic of this prohibition, it would make just as much sense to ban the the use of Machzorim (prayer books) on the first day of Rosh Hashanna when it falls on Shabbat. Curiously there is no similar prohibition when Yom Kippor (the "Shabbat of Shabbats") falls on Shabbat.
ML/NJ
This is about the shofar being blown in the temple mount. Rosh Hashanah this year falls on the Sabbath and Jews are not permitted on the temple mount on Saturdays. Hence, the petition.
Why Is the Shofar Not Blown on Shabbat?
https://www.chabad.org/library/article_cdo/aid/988699/jewish/Why-No-Shofar-on-Shabbat.htm