Why are you playing 4k movies on a 1080p projector??? Set the Apple TV box to only play 1080p movies.
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If you have an Apple TV 4K Netflix sends an incredibly low bitrate stream for 4K content when you have a 1080p screen.
500 kbps Netflix 1080p H265 stream Apple TV 4K
3 Mbps Netflix 1080p H264 stream Apple TV HD
Netflix uses their own compression algorithm for their videos and it looks like it's just too aggressive for H265 1080p content. My TV is decent at up scaling 1080P to 4K so it does not look to bad but I could see where a 1080P projector will have problems.
Is there any solution for thus. I don't have the budget now to upgrade to 4k projector.
There are 4K to 1080P down scaling devices this way the Apple TV will get the 4K stream from Netflix and send 4K to the down scaling device.
I don't have a recommendation for one but there are a bunch on Amazon that should be an easy return if they don't work.