The problem with wearing robes in the muggle world was that Axel was used to being stared at no matter where he went. Either people watched because they recognized him from Quake, or they stared because subtlety was not really a word in his internal dictionary. Axel was not a man who liked blending in. He'd tried to do so back home, and it had made him --and their entire family-- miserable. And perhaps that was why he tried so hard to push boundaries and make a scene, because he'd experienced the opposite and hated it.
But regardless of the reason, he didn't exactly see an issue with what he was wearing, even in the muggle world. Sure, people noticed, but again, he didn't really notice enough to care. That is, until someone actually confronted him about it and pushed him into an alley.
"Well, usually, yes, but what's wrong with how I'm dressed?"