I like to leave my guitars out, otherwise I don't play them. I have a couple of wall hangings and stands all over the place too. Will hanging a guitar from the wall damage it at all? Warp the neck? etc.
It won't warp the neck. The force of gravity on the neck is much less than the force asserted on the neck by those strings under tension.
I would still not advise long term storage of guitars by hanging them on the wall.
The safest place for your guitar is in its hard shell case.
While hanging on the wall your guitar is far more susceptible to changes in humidity and temperature. And these changes can definitely have an adverse effect on the wood your guitar is made from.
You can also experience finish issues with some nitrocellulose-based finishes when they're left in contact with rubber and foam, such as you might find covering the guitar hanger's hooks, for any period of time. It can discolour the finish and even rub it off the guitar with little effort.
And then there's the accident factor: a guitar hanging on the wall is far more likely to be bumped, banged, knocked, touched, dropped, sneezed on, puked over, drooled on, viewed by potential theives...you get the idea. It's just not wrapped in the layers of protective foam and plywood that a case provides.
Left mine in a stand that hung by the headstock when it transitioned to summer it caused a slight twist in the headstock. Gave the truss rod a small twist and it corrected some after a week in its case it's mostly back to where it used to be without any affect on tension and intonation. Be careful.