During the reign of Holy Roman Emperor Rudolph II the Ottomans waged a campaign in Hungary from 1593 till 1606. During this war when Rudolph II gained control of Protestant towns he confiscated property and converted Protestant churches to Catholic churches.
Were similar acts of religious intolerence occuring in the Protestant territories conquered by the Ottoman Empire? Were the Protestants of Ottoman-occupied Hungary and Transylvania offered more/less religious freedom than those in the HRE?
Early Modern Hungary in the time period that you described is great for your question because at this time Hungary was divided between Ottoman-ruled Hungary and Habsburg-ruled Hungary. Because of this we can compare how the different sections of Hungary treated their Protestants literally side by side.
The Ottoman Empire in general was widely regarded as being tolerant to non-Muslim faiths, and as the Hungarian Protestants were considered a sect of Christianity by the Ottomans, they did find themselves less persecuted than under their ex-rulers the Habsburgs. However, I wouldn't go so far to call their treatment as tolerant, but more that the Ottoman's were indifferent as long as the Protestants (or Christians, as the Ottoman's viewed them) followed certain rules. These rules included:
If these criteria were met, non-Muslim communities were allowed a certain level of autonomy, provided they recognize the Ottoman monarchy and administration as their overlords.
Under the Habsburgs, Hungarian Protestants faced persecution similar to other Eastern European states that were involved in the Protestant Reformation, such as Bohemia. Specifically, the Habsburgs targeted Anabaptists and Sacramentarians, despite the latter being publicly supported by local Lutheran estates.
This persecution included the prevention of Protestants being able to practice their faith publicly or collectively, imprisonment and hanging for speaking out against the Church, the closing or burning of Protestant churches, and Aristocrats forcing their underlings to convert to Catholicism. When the counter-Reformation was launched, almost all of Habsburg controlled Hungary was convinced to convert back to Catholicism or forcefully converted.
It is believed that the Protestant population in Hungary maintained their numbers because of Ottoman governance. By the time the Great Turkish War occurred in 1683, the Thirty Years War had ended and the Treaty of Westphalia was signed.
Sources:
Kontler, László (1999). Millennium in Central Europe: A History of Hungary. Atlantisz Publishing House. ISBN 963-9165-37-9.
Daniel, David P. (1992). "Hungary", in Pettegree, Andrew (1992); The Early Reformation in Europe; Cambridge University Press; ISBN 0-521-39768-5.
"Conversion", Tijana Krstić, Encyclopedia of the Ottoman Empire, Ed. Gábor Ágoston and Bruce Alan Masters, (InfoBase Publishing, 2009), 145–146
Ottoman sultans always liked the prostestanism.In his letter to Elizabeth II , Murat III mentiones similarities between islam and protestanism and offered an alliance against catholic spain which is seen as idol worshippers by him because of all those depiction of jesus in their churches.