There are several visibility settings. There is a setting for the entire household and then there are settings for individual items like the address, phone numbers and emails. If the entire household setting is limited then you can't set the individual settings to something more visible.
So go to https://lds.org/Directory
, click on 'My Household' and then click on the edit button at the top of the right side. Immediately under the edit button it should show your Household Visibility Limit with a link to edit it.
If you try changing that setting and it still doesn't save then there is probably some problem in the database and you'll need to have your ward clerk contact Local Unit Support and have them take a look.