You can publish a single-GIF post on Facebook and the GIF will be animated. As soon as you add more than one image (GIFs or any other supported formats), none of the GIFs in the batch will be animated.
GIF format is accepted on Instagram. However, it won't be animated when published via the API.
You could use a similar hack as mentioned above in the 2nd paragraph TIP.
GIF format is accepted on Twitter and animated GIFs are handled well.
Please check the following recommendations for uploading animated GIFs on Twitter:
Resolution should be max 1280x1080 (width x height)
The number of frames should be a maximum of 350
The number of pixels (width * height * num_frames) should be a maximum of 300 million
GIF format is accepted on LinkedIn. A GIF image will be animated when published.