I had a similar problem logging in via Safari. The problem might not be with the Google or Safari. The problem might be that you are already signed in to airbnb on your phone, via your Internet Service Provider (ISP) and that the app doesn't know how to sign you in again.
To see if this is the problem, go to Google Chrome on your phone; type airbnb.com; check to see if you are aleady signed in (I was and I have no idea how that was the case, but it was); if you are already signed in this way, via your ISP, go to the airbnb logo on the upper left side of your phone, in order to reveal the drop-down menue, where you'll find the option to LOG OUT. Log out of airbnb.
Go back to the home screen of your phone, locate the airbnb app, and sign in using your username and password. It should recognize your credentials.
Good luck
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Here was my answer to Safari users (same answer, different ISP):
I had this problem too, on my Iphone 5S. I kept getting an error message that said, "these credentials don't seem right" (or some variation of that. I spoke to an Airbnb rep for a while, and this is what finally worked:
Assuming that you have Safari on your Iphone:
1) go to Safari and click on it.
2) type airbnb.com into your URL/browser on your iphone
3) you should discover that airbnb is already open
(at this point, you can just use the site from here, or, if you prefer to resolve the problem with your app, which I highly recommend, assuming that you know your username and password)
4) click the airbnb icon in the upper-left, to access the menu to log out, and LOG OUT.
5) Hit the round home button at the bottom of your iphone, locate your airbnb app and enter your username and password.
This worked for me. The issue apparently was that airbnb was already open on my phone's url, and couldn't figure out how to open via the app. at the same time.
I hope that this helps.