Is it true that the singing group Abba has been supportive of the Palestinians?

No. There is no evidence that ABBA as a group (or the individual members) have taken a public stance one way or the other about Palestinians.

Where did you hear this rumor?

I hope so.

I've never heard about Palestinians but ABBA really denounced all the regimes which oppress the freedom of speech etc. There was a TV program called Let Poland Be Poland (found on YouTube) where Benny and Bjorn expressed their anger towards what was happening at that time in El Salvador, Chile, Afghanistan, Iran...