It is safe to disable Avast! online security as an add-on from within firefox. The only protection disabled would be phishing protection, site ratings, re-direction to open safezone in pro, internet security, premier versions, and some privacy protections such as ad blocking, web analytics, typo squatting protection etc.

Full malware protection is provided with or without the add-on, based solely on web shield.

From what I see, it seems that stackoverflow webpage causes the add-on to bug out. However, other normal sites like avast home page does not cause this.

Edit: phishing protection is partly provided by web shield beside that available in the add-on.