Just in case the issue is unclear to anyone, let me give the following example Sims, who each appear in the Gallery.
Dee Fawlt uses content from no packs, only base game.
Vanna Pyre uses content from the Vampires Game Pack and nothing else.
Miranda Made uses content from the Island Living Expansion Pack and nothing else.
Cyrus Wren uses content from Vampires and Island Living.
The first three Sims work exactly as expected. If no boxes are checked, Dee is the only one that appears. Vanna will appear when the Vampires box is checked, but not if it isn't. Similarly, Miranda will appear if the Island Living box is checked, but not if it isn't. The problem is Cyrus.
Say we have a user named Drake. Drake has the Vampires pack, but not Island Living. Drake checks the "Show Owned" option, expecting to see content he can use in his game. Dee appears, Vanna appears, Miranda doesn't... and Cyrus does. But Drake doesn't have enough content to use Cyrus in his entirety; some parts of Cyrus will be disabled if Drake downloads him.
Another user, Ariel, has Island Living but not Vampires. She has the same problem: Cyrus appears when she's specifically looking for Island Living-friendly content.
Barring hashtags - which are often abused - there is no way to configure the search so that Vanna appears without Cyrus (ditto Miranda without Cyrus). Cyrus (and other content like him) will absolutely clutter up the search results of people who can't fully use him. The only way Cyrus won't appear is if you happen to uncheck each and every last box that contains content that he uses, a problem that multiplies quickly - a LOT of Sims or houses use content from many different packs. If a house has an item from every single pack in it - not exactly unreasonable - then the only possible way to make it go away is to uncheck every single box, giving you only base game content.
What I'm suggesting is that, if you uncheck a box, everything that contains content from the corresponding box is removed from your search results. Dee, Vanna, and Miranda will work no differently, but Cyrus only appears when BOTH Vampires and Island Living are checked, not one or the other.