I have windows 10 pro and all my browsers are showing a transparent background (IE11, Edge. Firefox & Chrome).
I also have an imac (macOS High Sierra 10.13.4) and all browsers on that show your images as transparent also (Safari, Firefox and Chrome).
My devices iphone5s and iphone7 also show the image backgrounds as transparent.
I think we can deduce from the above that the problem lies at your end somewhere
It's either a cache (or corrupted cache) issue or a problem with your monitor perhaps. You may need to delete all your cache and history properly and not just f5 refresh.
Alternatively load your images into your paint editor (photoshop etc) and just double check they are not corrupted in any way and are showing correctly in the paint package. If so then re-save them under a different name and upload making sure you change the names in the html also. In this way you will determine if it was a cache issue or not and rule that out from the debugging stage.
Note that gifs only have index transparency and you usually have to select the 'matte' colour that you want to be transparent in order to get a smoother background. I generally avoid gifs where transparency is required and use pngs instead although they are a higher file size (unless its a very simple image). If your gif is always to sit on a white background then make the background white and don't worry about transparency.