The majority of Israelis despised Shulamit Aloni. She was considered to be an enemy of Israel and the Jewish people. If that is what the writer means as influential than yes, she had a great influence on people. Israelis hated her and her support of OSLO led to the deaths of many innocent Israelis and Arabs. Other than that I am not sure one can say she had any influence. I think she once pressured the mayor of Jerusalem to open a Non-Kosher Mc Donalds in the heart of Jerusalem. That's the most influential act I think she carried out.
Palestinians report IDF airstrikes on Islamic Jihad targets in southern Gaza Strip (Haaretz)
from the article: Shulamit Aloni: Israel's most influential woman politician