What is anti-democratic about trying to assemble a coalition to change lawmakers' minds and get them to vote differently? It is rather core to democracies that decisions aren't set in stone and if you disagree with the majority you can always try to renegotiate.
While most greens and progressives may be against this particular law, I rather doubt that if they introduced a progressive green law for a vote and failed to get a majority, they would immediately give up and never try to get such a law passed ever again.
And I think it's good that nobody has to give up on politics just because they lost once.