Actually, what you need is a different symbol for "disagree".
What do people viscerally (another fancy word) associate the Big Red X with? It's the teacher marking an answer wrong. So it's a double whammy. The user of the X is assuming a superior position, the teacher, while not so much disagreeing as saying, "you're wrong!"
You might want to consider one of these if you're not locked into the X by the software package:
https://www.google.com/search?q=disagree+emoji&tbm=isch&source=iu&ictx=1&fir=UztpVTm6p-SlMM%3A%2CHAyLR7-j6iDDyM%2C_&usg=AI4_-kRF5sizeF_6fJ6pw-Prll8x3R3ZSQ&sa=X&ved=2ahUKEwjIh62Dn4TfAhUILK0KHQB1CIoQ9QEwAHoECAIQBA#imgrc=UztpVTm6p-SlMM
I'd go with this one:
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Dunno if you have to pay to use it.
Personally, I don't care, but it might help solve some headaches.