The in-universe term for real ninja is "Anbu". Why does no one complain when One Piece does this?
Maybe it's because Oda is much, much crazier. But then, why do they call the non-ninja, ninja?
I haven't followed One Piece in ages, so I guess I don't see the exact point you're driving at - for me, they sure ACT like pirates. Sure, they have crazy powers, but they go around a mostly seafaring world in ships and curbstomp people for a living.
They do when they're forced to diversify into the sole military of a country. And in a world where people with weird bloodlines exist and can do these things, they'd be crazy not to recruit them.
Explanation?
Anbu don't wear them. Other ninja are organised like a military, so they need some kind of uniform (this one has the advantage that it can be quickly removed). There was one episode of the anime where the characters act shocked that someone would use a fake headband, but that was filler written by the animation staff. False flag operations happen all the time.
But it still feels stupid. Why would ninja identify themselves AT ALL? Rule number one of any stealth-capable operative - DO NOT LET YOURSELF BE IDENTIFIED.
Why not? Not that anyone does that in Naruto (they have fairly advanced technology, but no industrialisation).
Cellphones provide the enemy with an excellent means of locating you. Unless you're using a satellite cellphone, which is pretty bulky.
I've read some of the manga. It has cheerful ninjas with katanas who carry cellphones. Confused (and a protagonist who wants to be a "Hokage", but that's not really relevant)
Read on. The protagonist becomes increasingly less cheery as he runs into more and more of his unknown past's dirty secrets. And the only guy who DOES have a katana ain't a ninja, he's a bona fide swordsman (some might even say he's samurai-ish). The main character and the one who wants to be his love interest are the real ninjas of the cast (not counting Kagehoshi, as she only becomes an integral part of the cast much, much later). Then there's the gentle giant, the smart-alecky kid and the aloof swordsman. Almost everyone else they fight against has more ninja in them (exceptions made to the technofreaks they run into now and then).
Flame of Recca is often compared to Yu Yu Hakusho, so I suppose it's easier to understand if you've read some of that too.