This all sounds horrific and I really feel for the local businesses and tourists alike.
If it's man-made pollution - rather than a simple algal bloom - then tracing the cause(s) could be a long, protracted process. Once traced, eradicating those causes might also prove difficult as disposing of whatever it is that's causing the green stuff in a safe / more environmentally acceptable way might be a lot more expensive than those creating the problem can afford.
I've seen a few references to this situation in UK press / internet since booking our holiday a couple of weekends ago. Although I'm not yet sufficiently concerned to re-book somewhere else, if the pollution is genuinely harmful and if the seafood / fish is caught locally and sold in the market / served in local restaurants, it's easy to see how it might actually cause (or be wrongly blamed for) illnesses.
I really hope that the Turkish government fully engages with this situation and sorts it out as quickly as possible - for the locals more than anything - as most tourists won't take risks with their / their kids' health.