"Birthright" was originally set up for the unaffiliated and uneducated secular American Jew, it was not intended for the religious. However a very large number of the applicants are Orthodox and so the organizers set up a program called Maayanot for religious tours. Maayanot is targeted to the "Modern Orthodox" or "Young Israel" Jew, not the Hasidim.
Now, even though my family is Hasidic, the program did work out very well for my son. I don't know if it would be a good influence for my daughter, unless she could just skip the tour and head directly to Tzefat to her sister.
Now if the Satmars and the 'Snags want free tickets to the Holy Land but don't want their little darlings exposed to (gasp! horror!) Zionism, let them set up their own tours. If they are so repulsed by Zionism, maybe they can get George Soros to bankroll the project.