Could not confirm on my Android phone using 2 different mobile browsers. Issue appears to be isolated to Apple products. Do either of you have an Android to test to see if issue is there as well?
As I have no Apple products and it can't be confirmed in emulation (wouldn't be able to use anyway as I do not have a mac) I am unable to confirm and have no idea what exactly I'm looking for as a cause.
If possible install a different browser on your Apple product and see if the issue persists. For example install mobile Chrome or Firefox if possible.
That dropdown is powered by Bootstrap as it's a navigation dropdown to toggle the child content display. CB doesn't load this, but CB does load jQuery and if Joomla didn't namespace their Bootstrap into a noConflict jQuery it could be a conflict (unlikely due to load order). I see one very extremely unlikely conflict in cbTabs jQuery, which is loaded on the page having the issue on our test site, but I highly doubt that's it (will test it anyway though).