If you lose approval, then you will not have any romantic connection. I'll tell you more, if the approval drops too low, then your companion will leave you, at best, at worst, he will try to kill you. I believe Astarion and Lae are capable of this.
The system is not new, as far as I know, an approval system is also used in games like Dragon Age.
Personally, I am completely satisfied with this system. For example, Lae approves of cruel actions, if you are a soft-hearted and kind paladin, then I strongly doubt this will attract her to you. It's not even about a romance, but about respect, about friendship etc. It is quite natural that companions are annoyed by actions that they themselves consider stupid.
I know there is a way to avoid this, if you choose this "stupid act" when talking to an npc for another character (companion), then you will not get "disapproval", but there will be no "approval" either.
I am sure at a neutral approval it will be possible to build a weak romantic relationship. For example, you can sleep with Astarion or Lae having a rather low approval rating, but I am sure in the future it will show itself in a bad way.
There is also Gale, who can be bribed...