Does the RSPB count? I am a member of that.
I'm not a member of the RSPB, but if my memory serves me right (I'm sure RSPB members will correct me if I'm wrong) the RSPB has during recent years supported the culling of the ruddy duck, due to its tendency to hybridise with an endangered Spanish duck, and the culling of hedgehogs on certain Scottish islands, due to their tendency to eat the eggs of ground nesting birds, many of which are endangered species. Both species were introduced by man (the hedgehogs were introduced on the relevant islands) and both ruddy ducks and hedgehogs are popular and cute.
It is a dilemma that all conservation organisations have had to face from time to time when a native species has been threaten by an introduced species. Do they support the controlling of the introduced species, which may well mean culling, or do they support letting nature take its course, which may result in the extinction of the native species?