I am a member of Green Peace but I understand the complaints against them.
I would recommend a group like the Sierra Club. Low on controversy, lots of local chapters in case you want to become active and a good solid reputation with low overhead costs.
I don’t know what area you live in, but in the NY/Hudson Estuary area is the group Clearwater and the sloops clubs scattered about the area. These groups have achieved many real results at low cost and low controversy and successfully put on annual festivals.
I am a member of every group I mentioned.
You might want to look into what groups act locally in your area. One of the best things is to get out and participate in the programs. Go to the meetings; help with the clean-ups or demonstrations. Help put on a festival.
I have had a chance over the last 18 years to meet Pete Seeger and Bruce Springsteen, that is kind of a cool bonus.
Clearwater was instrumental in cleaning up the Hudson River and educating thousands of kids about the environment. Monmouth County Friends of Clearwater help force our counties biggest polluter to clean up its act and worked in a coalition to stop a Garbage incinerator from being built.
It can all be quite rewarding.
WWF is another good organization.
I think part of your decision should be what aspect of the environment you are most interested in making a change in. For me it was Clean Water & Air and now it is Global Warming.
There is a common saying among many Green Groups.
**Think Globally and Act Locally. **