*ironically, meaning that while most people in Lakewood support Israel, it's not expressed in a manner of overt Zionistic patriotism. So someone wearing an Israeli flag is assumed to be doing it "as a joke".
Depends what you mean by "support Israel"
As I understand it, from my upbringing and from my chinuch (45+ year in Lakewood and Lakewood type yeshivos)
Lakewood, and the Yeshiva World in general believe:
Eretz Yisrael: Every inch of land is Holy.
Secular Zionism: Bad, at times - evil.
Religious Zionism: Misguided
Establishment of the State of Israel: Mixed feelings. Might have been a necessary evil.
Holiness of the State of Israel: non existent.
The Flag: Zero religious significance, a symbol of a non Torah (and often, anti Torah) based political entity.
After the fact, publicly support the security needs of the State, including the IDF: Absolutely.
Not really looking to debate the merits of any of these points. Just clarifying what I believe the general mindset is.