If I attack someone that still has shields with my ION Cannon and it hits does the defender take the damage via the damage cards and is ionized or does the defender clear the hit with a shield and still is ionized?

I'm only using the ion turret card as a reference, but it does say that the defender suffers 1 damage and receives an ion token. That would mean that if the defending ship has a shield token it loses one. If it only has hull left, then it takes a face down damage card. If the card said "deal a face-down damage card", then you would deal a card regardless of shield value.

Ion weapons do generally not bypass shields. For Ion cannon you deal 1 damage to the shield and 1 ion token

Do what the card says.

The card says they take 1 damage. This removes a shield if they have any left, else they are dealt a damage card.

Then the card says they take an ion token. No conditions, nothing about not assigning it if they to the damage on shields. So regardless of shields, they get an ion token.

Also, note that gaining the token and being ionised are not necessarily the same thing - a large ship hit with a single ion cannon is not ionised until the second shot hits it.