What is the reason that during Shabbat/Yom Tov benching, some people say the "Tehillat Hashem" paragraph and some don’t? I once heard some sort of historical reason where when the state of Israel was formed, the anti-zionists added the paragraph in for whatever reason... Is that valid? Also, how come it seems like in Israel itself, most people do not say Tehillat Hashem, while in America, it seems like more people say it?

I don’t know the source of these four verses though the first two are also found in the Sephardi Siddur; I doubt it has anything to do with the Zionists. I have seen a commentary that relates the four verses to the four blessings of Birkat HaMazon. (Ozar Taamei HaMinhagim 3) Some have the custom to say them and some don't.