To amend Nick's answer: Gif images only support 1-bit transparency. It is either on or off, with no in-between transparent values possible. And as such, when you export a semi-transparent pixel to Gif, the software must multiply that pixel with the background matte colour (which in most software can be selected during export).
The result is often a white aliased edge surrounding the graphic where the original semi-transparent anti-aliased pixels sat.
In short, it is a limitation of the Gif format. You will always have to live with aliased edges where the edges meet transparent areas in Gif.
The most acceptable solution is to switch to APNG (animated PNG) instead, which is supported in all major modern browsers, including Edge. APNG does support partial transparency.
Of course, with Adobe traditionally lagging behind the times, users can rely on AnimateCC not supporting output to APNG, and you will have to export your animation as a PNG sequence first, and then use a converter to save an APNG animation.
Some suggestions: http://littlesvr.ca/apng/
Support for APNG is now at almost 90% global:
https://caniuse.com/#search=apng