I just received an answer from Yubico about my problem.
Quote:
Hello Sybren -
Thank you for contacting Yubico Support. We have sent a few test NEOs to the developers of Password Safe to look into why the keys won't authenticate when U2F is turned on with OTP. You may want to consider temporarily disabling U2F so you can use Password Safe and the Windows Logon Tool. As we don't control Password Safe, we can't guarantee if/when this functionality will work.
Regarding the Logon Tool, we have notified our development team of the trouble you are having, and we've also confirmed we're seeing the same behavior on our end. We hope to have an answer for you by mid next week on the Logon Tool. We have marked this case for followup and we will contact you next week to let you know what we've found, and determine if we need to release a new build of the Logon Tool.
Best Regards,
Yubico Support Team
I hope some of you find an answer in here as well.