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Not sure if this works for all macs but this solution worked for me (2021 M1 Pro MacBook). Last week I tried streaming a game (Stardew Valley), and while the game ran perfectly fine for me on my screen, the output from OBS was dropping tons of frames and lagging half a second behind.

To fix this: switch your source from Window Capture to Display Capture, set Crop "To Window" in Preferences, and set Window to your game from the dropdown (in my case [Stardew Valley]. You must have the game open for it to appear in the dropdown.

Window Capture is notoriously terrible on Mac OBS. For some reason Display Capture is much smoother, and since you can configure the Properties to crop to a window, it is functionally the same. The only difference is that the colors are slightly de-saturated on Display Capture (not sure why), but you can apply a Color Correction filter to adjust for that. For me I just bumped Gamma to 0.15 and Saturation to 0.30.

Hope this helps someone!