Between devices that are connected via HDMI, a so-called. Handshake must take place. In this process, the two connected devices meet. This is a very complex process in which the devices exchange a variety of information:
-Supported Resolutions and frequencies
-HDCP Certification and encryption (mandatory for HD output!)
-CEC Capability (Consumer Electronics Control)
-Audioeigenschaften (Bitstream, PCM, ...)
-3D Capability
-etc.
Target device and source device are "adapted to each other" so to speak, after a successful handshake.
You close now with such a Y-cable, a source device (eg PS3) at 2 target devices (eg beamer and TV), so the source device can not "know" which of the two target devices the handshake to take place!
At most, in two identical target devices could theoretically work. Even an alternating operation of the target device is a pure gamble, because devices are often detected in standby mode, but no correct handshake takes place.
Remedy can only create a real HDMI switch that separates the target devices when switching clean.