I'm not sure that O-sensei was able to separate the two things. I'm not saying that you must have Shinto beliefs, but I would say that you need some kind of understanding of them if you have any interest in trying to understand anything that the Founder said or wrote.
I agree. Furthermore, it helps to understand Omoto specifically. Their core belief is that there is only one God and this God manifests itself differently in different cultures. So when the fundamental Christian says that "I believe in Christ, the son, and God, the father. And all else is wrong", the Omoto believer (including O'Sensei) is going to think that that individual is mistaken. I think they will not be able to separate the two things as Chris has written.
To the person who says they just practice Aikido and are not interested in all that religious stuff, the Omoto believer is likely to be thinking something like, "Go ahead and keep believeing you are not doing the will of God. someday you will realize the truth."