I regularly train at two dojos (twice at one and twice at another) with the full blessing and encouragement of my primary sensei. He also regularly encourages other senseis at other dojos to be the guest sensei at the dojo while encouraging his students to try out new styles. He says that its important to have a braod base and not be restricted in the practice of aikido. IMHO, I thinks he feels that its all aikido with different interpretations and perspectives.
Yes stylistic differences can be a problem and it does take a certain amount of experience not to get confused. The dojos that I regularly train at are both aikikai but I have had the pleasure of training with some people in yoshinkan, yoseikan and kokikai.
My personal reasons: I get a different perspective on basic technioque and application and the greater emphasis on weapons with my other sensei.
As for getting confused, I would stick with the one teacher if you are a beginner until you get the feel and are comfortable with the way he/she shows the techniques. If you are an experienced aikidoka say with a 2 to 3 years under your belt (sorry no pun intended) it may be worth your while to broaden your horizons a bit. It may be easier in the beginning to stay within the same style too.
I have always been very open with my primary sensei and his senior students about this and he has been very supportive and encouraging as well. So no problem there.
I agree with loyalty to your sensei but if your sensei is concerned about improving your aikido, I wouldnt see that there would be a problem with you taking additional classes at another dojo. I think its important to practice the way it is taught at the specific dojo and not to get the two mixed up. Its really having an open mind and being receptive to the key lessons and principles.
Hope this helps and best for training