Re: Two teachers...
I agree with Lyle.
Also, I have a friend who told his new Sensei that he was going to be training in two dojos and he was promptly told that he wouldn't be doing that in "his" dojo. I also once trained in two dojos many years ago and I did tell my Sensei and he gave me permission but it later caused some minor problems. I once had two teachers in the same dojo from different styles but again, because of internal problems, which class you went to became problematic.
I think that the answer to the original question is that it depends on the circumstances. As George Ledyard said, everything should be clear and up front. I also think that in a situation between dojos of the same organization, things should be OK if all is up front and known and even in other situations where people are friends and are used to cooperating. That said, sometimes, Sensei's are wary of "dojo hoppers" and other political things. I personally don't try to regulate what the students do with their own time and would never forbid a student of mine to attend another dojo. I do think that getting your basics done in one style is preferable but if a person can take info and adjust , that's fine. It all depends on what the circumstances are and who the people are. In short, no one can answer this question. We can just report on our experiences.