I was using skinport for a long time and decided to install Animated Player mod and it doesn't work. I also tried with mo' bends mod, it still don't work. Someone have any ideas how to solve it?

The SkinPort will replace player model to display the player skin in newer format.
This will cause incompatibility with mods like those you mentioned as they also replace player model.
Sorry about the inconvenience, but it probably won't get fixed.