Is there a way to hide user notifications by category, such as informational messages?
As of this time this is not possible. This is a feature which might be implemented in the future. However, it is also possible to see detailed user notification information in the Calculation Summary. This opens after computing a model and can be accessed by going to Analysis > Calculation Summary.
You can then highlight the time step where an issue is occurring and see the user notification information in the Information tab. Other tabs in the Calculation Summary can be useful as well, such as for checking the status of an element (which a tank is emptying, for instance.
Different color's meanings in user notification & Calculation Summary