It's looking more and more likely that rumors stating that the iPhone 7 will not include a 3.5 mm headphone jack are true. Chinese websites Wei Feng and Anzhuo.cn reported that anonymous sources on the supply chain confirmed that the controversial design choice is a reality.
Both sites claim that Apple intends to release its own Bluetooth headphones (probably under the Beats moniker). Currently these claims are unfounded, and there is no evidence of a design for these purported headphones.
It's been speculated that Apple will sell an adapter to allow for wired headphone use. In all likelihood, this would eliminate the ability to charge and listen simultaneously—that is, unless their iPhone 7 has a wireless charging capability (that no doubt would also be purchased separately) or ships with two Lightning ports.
As much has been made about this, Apple traditionalists probably won't ditch the next iPhone over the lack of a headphone jack. The fan base has powered through previous unpopular changes, like the change to the Lightning connector for the iPhone 5.
The reports from China say that Apple may release Lightning-compatible earbuds. Third-party manufacturers have already released Lightning-compatible headphones.
If these rumors are in fact true, the initial outcry probably won't have too much of an effect on sales—Apple users are quite loyal to the company, to say the least. Maybe this changes the mind of people who were considering switching to an iPhone. Presumably, there will be a speckling of haughty blog posts and YouTube rants about how "Apple has gone too far!" But for the most part, it'll probably just be business as usual.