Cropping VR video afterwards I have mp4 SBS 180 VR videos made for Oculus Rift. I'd like to crop the videos a little (simulate the zoom) and then downscale to "cardboard" resolution so it would be smoothly playable on mobile devices.

Some mobile players have already zoom function built in, but this should work as a workaround for keeping the picture sharp (working down from the big resolution) at the expanse of FOV.

Pretty soon I realized I can't simply crop the whole video. I have to crop both sides separately and then join them together as they were.

Could you point me to video-editing software (preferably free and fast to learn) that would allow me to do such thing?
Using the mask image below, you can use ffmpeg to crop and output a MP4 with the visual content bounded in the same elliptical shape as the mask
ffmpeg -i input.mp4 -loop 1 -i 360mask.png \
       -filter_complex &quot;[0]split[a][b]; \
        [a]crop=iw/2:1522:0:300,crop=iw*0.8:ih*0.8,scale=960:-1,pad=960:960:0:150[l]; \
        [b]crop=iw/2:1522:iw/2:300,crop=iw*0.8:ih*0.8,scale=960:-1,pad=960:960:0:150[r]; \
        [l][r]hstack[c]; [c][1]alphamerge[ca]; [1][ca]overlay=shortest=1&quot;    vr.mp4

The video is split into two cropped halves to a rectangle which exactly bounds the visual area, then cropped to 80% along each of its dimensions, and then scaled and padded to a 960x960 canvas, rejoined to form a 1920x960 frame. Then the mask is applied to form the elliptical cut-out.
Mask


This is the basic technique. The visuals in your supplied image aren't centered, so I customized the crop expressions based on measurements within an image editor.