If you're interested, my two cents worth: I'm an animist. While Native American spirituality does appeal to me, I am not a member of, nor do I really try to emulate or use Native language or practices...although they have been helpful in connecting to my animism.
I can't answer for Christianity and Islam being animist, but I know of followers of both religions who do consider themselves animists to some extent.
For me, animism starts with the recognition that everything that exists is--at least potentially--is a "person" who is worthy of respect. There are all kinds of persons in the cosmos: rock persons, tree persons, fish persons, Moon persons, and so on. All kinds of persons, all deserving of respect. and all are usually considered kinfolk...they are part of our extended family.
Animists have relationships with their kinfolk...obviously, it's difficult to have a relationship with every single thing or kind of thing...but those persons we need for food, for clothing, for housing, for transportation, and so on, an animist will enter into a relationship, usually a ritual or set of rituals, to ask permission and offer recompense to those we depend on for food--those we kill, those we harvest, those we harm, and so on.
Are you an animist? Do you treat the objects in your house as if they are persons, kinfolk? Do you do the same with your food, thanking those individuals who you are about to consume for their sacrifice, and apologizing for having harmed them? Do you thank your computer or other electronic devices for their help?
If you do, you're probably an animist.
Hope this helps, and if you've got questions I'll be glad to try to help.
