It is perfectly fine to use animated gifs in any capacity you like in WordPress, even as featured images. When you upload an image, WordPress will process it into various shapes and sizes, as specified by your theme and possibly some plugins as well.

The version of image that gets displayed is determined by your theme OR, if not specified, WordPress core (thumbnail = 150x150). The image is then displayed by the theme with the function the_post_thumbnail() - by default, this will use the \'thumbnail\' size, which is generally the smallest size available.

To ensure that your uploaded gifs are displayed as uploaded (without any processing), you need to modify the_post_thumbnail() in your theme templates to instead read the_post_thumbnail( \'full\' ). This will instead use the original image with no processing whatsoever.