Airbnb does take a hard line against circumventing their payment system (thus denying them their fees). From their terms:
In connection with your use of the Site, Application, Services and Collective Content, you may not and you agree that you will not:
use the Site, Application, Services or Collective Content to find a Host or Guest and then complete a Booking of an Accommodation independent of the Site, Application or Services, in order to circumvent the obligation to pay any Service Fees related to Airbnb’s provision of the Services or for any other reasons;
accept or make a payment for Accommodation Fees outside Airbnb Payments. If you do so, you acknowledge and agree that you: (i) would be in breach of these Terms; (ii) accept all risks and responsibility for such payment, and (iii) hold Airbnb harmless from any liability for such payment.
Airbnb has the right to investigate and prosecute violations of any of the above to the fullest extent of the law. In addition, and as set in these Terms, Airbnb may take a range of actions against you, including but not limited to removing or disabling access to any or all of your Member Content or deactivating or canceling your Listing(s) or Airbnb Account, for a violation of this Section or these Terms.
They encourage guests to report such attempts to them. They do note that, in some cases, you might need to pay local taxes directly to the host though, so presumably they don't object if that is the case.
These rules prohibit circumventing Airbnb's booking mechanism, but as I read it, doesn't strictly prohibit all off-site communications if you still plan to book through the site. However, communicating outside of Airbnb has some risks.
In particular, you could be subject to a nasty phishing scam involving a fake Airbnb website. Such communications could lead to links that look like the real Airbnb website, but actually point to a decoy website where your personal information can be stolen. There are other types of scams on Airbnb as well, and sharing contact information to communicate outside the platform makes you more vulnerable.
Communicating outside of Airbnb also may make it harder to take advantage of their guarantees. If you exchange messages through the site, they will have a record of exactly what was promised, which gives you a paper trail if something goes wrong. If you talk off-site, you'll have no proof of your agreement if things go south. For important details like whether your room will have a lock, I'd want to have a record of that promise in case I need to use it to cancel my reservation and get my money back.
After paying, Airbnb usually gives you direct contact information, as you'll need a way to organize logistics and an emergency contact.