The power of this subtle hyphen shouldn't be underestimated. With co-working vs coworking, it's the difference between working in the same place for the same company vs. mindfully working alongside others while helping to grow each other's business. It's the difference between helping to bolster someone else's valuation vs. helping your common collective good.
While the distinct differences in the meanings of words are all important, this one is particularly critical to how you view your workmates. Your relationship with a coworker is vastly different than your relationship with a co-worker. The loss of the hyphen represents the loss of the company that acts as the go-between you and your workmates in the first place. Without the company, you work with each other because you want to. If you don't want to, then you don't. That's the simplest distillation of what is great about running your own company. Many large companies will tell you to "run your business like your own company". That autonomy will quickly fade when you let a potential customer know they are not worth the hassle.
While the intent is obvious, there are a lot of hurdles to jump through in order to make the hyphen distinction happen. One of the frustrating components of this movement is seeing a well-written article about a great coworking space referred to as co-working. Even the spellcheck puts a red squiggle under coworking. But it takes time to affect change in the AP guidelines. Ramon Suarez's email to the AP Style Guide has been one of the requests, but there is still work to be done.
Until then, know when to use your hyphens. It will help to clear up the type of place you are working in and it may help to change your relationships at work.