Should management of invasive alien wildlife species depend on how cute the species is?

Invasive alien wildlife species are major problems for native ecosystems leading to pressures upon and even extinction of multiple species native to the local environs, threatening biodiversity and the local ecosystems. Governments across the world, with the support of scientific bodies and wildlife conservation advocacy groups, have put in place plans to deal with invasive wildlife species, inclusive of rapid eradication and control, for example, the EU’s:

Killing off some fraction of the population of alien invasive species is standard and should be done in manners that “spare avoidable pain, distress and suffering of animals during the process.” In general best practices for most invasive species does not include capturing some fraction of them, neutering them, and releasing them back into the environment. You would not, for example, see anyone saying that rabbits in Australia should be captured, neutered, and released as a serious proposal. But rabbits are not that cute, and other than Bambi, neither are deer.

There is generally little public outcry about the use of lethal means of population control of invasive alien species … unless the species is feral cats that is. Feral cats … hey kittehs are cuter than any of those 27 native Australian species that they have led to the extinction of. The lesser bilby, desert bandicoot, crescent nailtail wallaby and big-eared hopping mouse? Only a little cute. Invasive alien feral cats win. Suddenly celebrities conclude that the experts are wrong … but only for feral cats.

So opinions? Should feral cats as a species be handled differently than other invasive alien species that harm native ecosystems?

Before anyone goes there I do appreciate that we humans ourselves are the most successful invasive alien species of all. But I am willing to state that our populations should not be controlled by lethal means. If that makes me hypocritical I can live with that.