I attach a patch for this bug that takes the simple approach of adding SELECTION_REQUEST_EVENT to the list of events to ignore in kbd_buffer_store_buffered_event.
This seems simple and safe (it's not something one would normally consider an input event).
Further, at present it would not help helm to implement Eli's suggestion of a list of events for input-pending-p to ignore, as Helm currently does not use that (it has a custom version of while-no-input that does not call input-pending-p).
As a helm user with an external clipboard manager, I was experiencing this bug. I'm using Emacs with this patch currently; it seems fine, and I don't have the Helm problem any more.
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0001-Ignore-SELECTION_REQUEST_EVENT-in-while-no-input.patch