Twitter doesn't let you save the video neither.

One (cumbersome) way of saving the video is to open the tweet and prefix it with m. e.g https://m.twitter.com/github/status/917527674163167233 and then download video.

youtube-dl link to tweet from your terminal

That always results in desynced A/V whenever I try it.

Usually lots of errors like the following from ffmpeg, then the audio is about a second behind the video

[mp4 @ 0x98668b4620] Non-monotonous DTS in output stream 0:1; previous: 132227, current: 131204; changing to 132228. This may result in incorrect timestamps in the output file.

Shift+Right Click on Firefox should work.