Im not too picky about the era. I was hoping to get an answer including the evolution of the state but ill take any answers. I'm curious if it gradually evolved into a more secular state over time (like much of europe) or if it maintained an archaic religious view. If the latter is true, I was hoping to discover if these beliefs contributed to the fall of the empire.
Like I said before though, any answers relating to the title are welcome!
"Islamic extremist" is an incredibly vague and incredibly loaded term, and the Ottoman Empire is one of the longest-lasting states since antiquity. What do you mean by that term, and which era of empire are you asking about?
The short answer is no, not as you are probably picturing. As another user mentioned, the Ottomans were actually fairly tolerant to other religions, especially those who were "followers of the book." Since Christian and Jewish beliefs were similar enough to Islam (all are monotheistic and follow a specific book/Bible/Torah/Quran, etc.), the Ottomans had no problems letting conquered peoples keep their religious beliefs. That being said, they preferred people to convert.
Realistically, there were two options for people under Ottoman rule when it came to religion. 1. Convert to Islam. 2. Keep their faith, but they had to pay a special tax, a jiyzya, and submit to devşirme, or a blood tax. Essentially, Christian children would be chosen to be slaves to the sultan and would be taken, converted to Islam, and raised to become Janissaries, clerks, etc. But that's getting a bit far from your original question.
There's also some evidence that the Ottomans were not seen as devout Muslims as other Islamic states would have preferred. A lot has to do with what time period and who was sultan/in power to determine how devout the Ottomans were. I'd also recommend Colin Imber's book The Ottoman Empire, which covers the Ottomans and religion very well, however it is a bit of a dry read.
If by "Islamic extremist" you mean something like ISIS then no, absolutely not.
For most of its history, the Ottoman Empire had a policy of religious tolerance towards Christians and Jews. They did not have the same legal rights as the empire's Muslim subjects, but they were at least allowed to worship freely. That is more than can be said about some of the Ottoman Empire's contemporaries in Europe.