Yes, I took mine out completely. I’m not sure how the suggestion from Coldest Water to “wiggle it” or adjust it helps – it’s a solid piece of rubber that fits like a plug in the cap. Without the plug, at least you can drink like normal from the straw.
That clear plastic piece is a 1 way valve. If you take it off, your cap will leak. However if it is on too tight, it create vacuum which could make it hard to drink. Ideally this should be on, and allow for suction.. Simply adjust it slightly/wiggle it if it is on too tight. If you have any issues though we’re here to help – firstname.lastname@example.org