For some reasons, I feel my teacher is afraid of offending anyone at Aikikai Hombu, hence, the "dislike" for Yoshinkan, Iwama-ryu and probably Nishio. So, when I said he will not permit it means he will not permit it period - no discussion.
Personally I think you should find a Shodokan (aka Tomiki) Dojo.
If he dislikes Yoshinkan, Iwama and Nishio then by logic he should absolutely hate us. If you're gonna be an Aiki-Heathen, be a REAL Aiki-Heathen is what I say
So to my question: Disloyalty to who? My teacher or to Aikikai?
It can't be disloyalty to Aikikai since I know of many Aikikai instructors (and a couple Shihans) who are open to cross training within Aikido. Unless they are all heathens too.
If you want to be "loyal" to your teacher, great. But unless you signed an agreement to be "loyal to him alone and his one true path" when you signed up for classes, then there is no reason to stick around and limit yourself. Most non-ego intoxicated Instructors I have met are very open to their students "standing on their shoulders" and moving beyond even them. To do this one often needs a comprehensive view of Budo that allows the the more particular training in one's style to make a bit more sense when seen from an outside perspective.
From my experience Instructors who call for this sort of loyalty are either 1)Afraid that their quality of instruction is not up to the par of the group they are representing 2) Taking liberties in their own teaching methods that would be frowned upon if viewed by other teachers who know how to spot BS 3) So consumed with their own ego and belief that they are on the "one true path" that they view other training methods as being somehow "beneath" their own.
The above is just from my experience, for all of the above I'd be heading out the door. If you are worried about disloyalty the first question you need to ask yourself is whether you want to learn "Aikido" and be proficient in it or if you want to align yourself politically with a particular system of teaching and become an instructor yourself etc. etc. If your answer is the former then you do whatever it takes to be proficient (in your own view) in Aikido. If the answer is the second one, then you have to decide whether you want to be Aikikai affiliated or affiliated to your instructor (which at the moment is the same thing as being Aikikai affiliated, but may be only so for the moment). Often the "I am the one true way" sorts tend to get antsy when their overseeing organisation is not going where they would like it to.
So its your call - Politics or Proficiency? Sometimes you can get both in the same place, often not.
Just my take. I reserve the right to be wrong.