Projector only displays one color
Macbook doesn't have VGA built in, so normally everyone is using DisplayPort to VGA Adapter, which is actually converting digital signal to analogue. The issue might be with converter itself, but if you are saying it's bad only with the Projector, but works with everything else fine - then I assume that Adapter is ok.

I'd suggest you to troubleshoot in order of appearens:


Adapter.
VGA Cable.
Connection slot or pins on the projector input.


To check the adapter is easy - try connecting via different vga cable to any monitor which has it. To check VGA cable you are using - try connecting it to different device, for example other projector or monitor. Clean the pins in VGA slot of projector, it might be some dust got in from ventilation, or whatever.

The single color to me sounds like it's bad contact somewhere, a VGA cable is broken, or with pin connectors. This happens normally when you have analog cable, alike VGA, when one/several color components goes off.

If you projector has other inputs, DVI or HDMI - I'd recommend to use them, instead of analog VGA.