To reply to any Tumblr post with an animated GIF, the GIF you are using must abide by Tumblr's image size restrictions. This means keeping it below 1MB in size and no more than 500 pixels wide. While you can upload images that are slightly over the resolution limit, they will be automatically downsized upon posting. However, if you can't resize your GIF or it is being resized when it shouldn't, there is a way to work around the automatic resizing.
Post GIF Reply
Adding an image reply to a post you're reblogging is the same as uploading an image to any post you make on your own. Scroll to the bottom of the text box and position your cursor to start a new reply. Click on the camera icon to insert a picture, select your GIF and then click "Reblog." The only exception is when reblogging image posts; in this case, you need to upload the GIF to an image host, then copy the image's URL into the box that appears when clicking the camera icon.
Post Without Resizing
Tumblr may sometimes resize your image reply, and it may turn it into a grey thumbnail, forcing users to click on the thumbnail to see it. This can be avoided by copying the image's HTML code into your reply from a new post. Open Tumblr in a second tab apart from your reply, start a new text post, then upload your GIF. Once uploaded, click "<html>," then copy the URL of the image you just uploaded. Go back to your reply, click "<html>" on that post, paste the image URL and reblog the post. Your GIF will show up without being hidden in the comment tree and every subsequent reblog.
- Jupiterimages/Photos.com/Getty Images