White dots around transparent GIF

The white pixels are caused by the transparent anti-aliased edges left behind when you cut out the animation.

Gifs support only 1bit transparency: either on, or off.

Transparent smooth edges are impossible in GIF, and Photoshop attempts to reduce these to 1bit by dithering the edges and introducing a matte colour (in your case white, which is the default) as well.

This results in the white halos/pixels.

You have two options:

1) remove all transparent smooth anti-aliased edges, and create aliased edges instead. You may have to redo your selections and ensure no anti-aliasing is used. Hard pixel edges only!

2) avoid the archaic GIF format altogether, and switch to an APNG (animated PNG) instead. APNG supports full transparency. All web browsers now support animated png files.

The problem is that all Adobe apps are unable to export animated png files.

The simple solution: export your animation as a PNG file sequence, and assemble these into an APNG file with either one of these tools:

PNG Assembler (Windows)

https://sourceforge.net/projects/apngasm/files/2.91/apngasm_gui-2.91-bin-win32.zip/download

APNGb (Mac)

https://github.com/shgodoroja/APNGb

Yes you need to delete the pixels you can not use multiply blending or blend if for you need the other white pixel to cover the background