Question: Why are some shuls decorated with flowers on Shavuos, and some shuls not?
Answer: The Rema (OC 494:3) writes that many have the minhag to place herbs in shuls and their homes over Shavuos to commemorate the giving of the Torah. The Mishna Berura (494:10) explains that there was grass or herbs on Har Sinai (See Kaf Hachaim OC 494:53).
The Magen Avraham (OC 494:5) extends this minhag to trees, writing that as we are judged on Shavuos over the fruit, the trees should remind us to pray for a good produce (See Shulchan Aruch Harav 494:15). R’ Ovadia Yosef (Yechave Daas 4:33) quotes midrashim to explain why people place flowers.
The poskim (Chayei Adam 131:13, Mishna Berura 494:10; Igros Moshe YD 4:11:5) quote the Vilna Gaon who decried the practice of placing trees in shuls as it has become the practice of idolaters. Thus, some shuls don’t place any plants in their shuls (See Aruch Hashulchan OC 494:6).
R’ Ovadia Yosef (Yechave Daas 4:33) explains however, why this isn’t a concern and writes that this is an important minhag. Additionally, it seems that while the Vilna Gaon disapproved of laying out trees, there would be no issue with herbs and plants (See Kaf Hachaim OC 494:56).