What is the make/model of your receiver? If you have a home theater receiver that has HDMI switching and signal pass through, you should have no issues hooking up whatever you have to the receiver and then using one HDMI cable from the receiver to the projector. As follows:
PS4 output > receiver input GAME (or whatever you name it on the receiver)
BD player output > receiver input Blu Ray
Receiver output > projector input
The only signal your projector should receive is video unless the projector itself is designed to play sound. If that's so, disable it and let the receiver do its job. If, however, your home theater receiver does not have the capability to stream out, then you're going to have to do something like the following:
PS4 out > HDMI switch input
BD out > HDMI switch input
HDMI switch out > projector input
Projector output > receiver input
Lastly, and perhaps the biggest and most relevant yet confusing question here is, why are you using a BD player when your PS4 has one built in? Adding in the BD player is only complicating your setup.