When it comes to Aikido specifically, I do not believe that you can separate the martial and the philosophical and still call it Aikido.
Strictly speaking, I think I disagree. I look at the variety of Aikido practice that I've seen, which spans from being almost entirely physical in emphasis to almost entirely mental/"spiritual," and I think all can call it "Aikido," because they're derived from the lineage of the same name.
I look to my experiences with Jinja Shinto as an analogy. My sense is that individuals will pick up different meaning and that on some level this reflects the individualized nature of one's connection to spirituality/kami. Similarly, I see Aikido as an expression of nature and that different groups of people will naturally connect to different aspects of that whole. This isn't to say no one can be wrong in their understanding...and indeed I think on some level no one can be absolutely right...probably. Hence the path of learning being one for a lifetime, a continual process of applying new information and refining the old, through focused interaction. As a
I get the sense it ultimately has to do with how to understand the broader nature of things and I think that demands a little individual wiggle-room or it risks becoming a kind of faded photocopy.
...My two bits.