Ever since the update I cannot share my screen with the person I call, but they can share their's. The option appears as unclickable. What's going on with this?
If you have not yet updated your Skype to the latest 188.8.131.52 version and your contact is in “Invisible” state, then this may be the reason. Due to a bug in the 5.8 version, screen sharing was disabled when a contact was in “Invisible” state.
In Skype go to Help -> About Skype. What version is reported?