Not sure if this is already a known bug, couldn't seem to find any other issues on this.

This has been present in every version for the past few years at least. Always the first 2 frames are rendered with the Alex skin, then the 3 frame and onwards are the correct skin.

Tested on multiplayer and singleplayer with perfectly consistent results.

Attached are 3 screenshots in render order.

That is unfortunately just how Minecraft works. It loads the skin for every player entity in the background (even when it was previously loaded). I've opened #634 to improve that specific behavior.
There's also a bunch of other things which aren't quite right immediately after restarting a replay (cause they don't need to be for regular game play, no one's going to notice there), a way to work around all of those is to simply jump to 10s before the path starts, then play the replay for 5s and then start the render. I'm also considering automating that procedure, though I'm not yet quite sure how to do that without forcing all renders to be 10s longer than they'd need to be.