1. Do you feel it is a legitimate halachic opinion to reject the legitimacy of the modern day orthodox rabbinate?
2. Where does the modern day orthodox rabbinate draw its legitimacy?
3. Can you offer a good resource on the halachic development of conversion?
4. Is the rabbinate a purely political institution?
Here are some answers to your questions:
1-2 The rabbinate, no matter which type, draws it legitimacy and is considered legitimate is so far that it is loyal to the divine torah that we received on Mt. Sinai, which includes the written law in the bible, and the oral law (the mesorah), which is the Mishnayos, and the talmud. To the degree that ones halachic opinion is coming from the torah and the mesorah, it is legitimate, and whenever it is coming from interests to change the torah or “adopt” it to what is convenient for us it is not legitimate.
3. Tractate Bechoros 30b, Rambam (Maimonidies) Eisurei Biah 14, Tur and Shulchan Aruch Yoreh Deah 268, Igrot Moshe Yoreh Deah vol. 3- 106, 108
4. I don’t know what “Rabbinate” you are referring to.