I think the discussion started about projecting digital images at a camera club. The premise was jpegs would be submitted and the question was about requiring a color space (sRGbB, aRGB, etc) and what to do with ‘untagged’.
Alan Klein mentioned a laptop. If the laptop was a PC (I’m lost about Macs), free software such as Irfanview and Faststone are “color aware” and will recognized the jpeg color space and convert to the color space of the monitor profile. I believe (not sure) if it is ‘untagged’, they will assume sRGB.
The biggest problem is the projector. I have seen really bad projection setups, better ones, but never good ones (I'm sure some professional setups do, but I have never seen them and have seen some people really try).
As I understand it (limited knowledge admitted), projectors are really difficult to profile properly. Then, most laptops (at least PCs) do not usually have graphic adapters which can support two profiles (projector/2nd monitor and built in monitor) and most free software is not built to support dual output. At best, the user can set the display profile to the one for the projector, but rarely do this as the monitor screen will then be off.
Possibly Andrew can provide advice to Alan and the OP on what best software to use how best to set up a projector on a laptop (when provided with what hardware and OS is used).