Will a Youtube video with clips from a copyright protected anime website (AnimeID) be taken down even if I give credit in the video and description?
An algorithm decides that. It can go both directions. The system is not smart enough to correctly decide if your video meets the cirteria for fair use/citation. In case of a wrong decision you can appeal and sometimes you succeed.

If you give credit or not does not play a role for Youtube, however it's a legal requirement for correct citation.

If a copyright violation is detected, the video either gets blocked or the income will be redirected to the holders of these rights. And you get a strike.

Funny: As I write this I'm listening to an experienced Youtuber in a live stream and by chance she speaks about this topic and says: "It's a game of luck if you get a copyright strike or not." I think this confirms my point.