After Effects and Photoshop: color change after render

Nah, this will never work. You will need to talk to your client. It's technically unavoidable. This is the same old nonsense video designers had to put up with for decades. It's going to fail and if you're unlucky you may get the color right, but still get complaints because your customer views your work on a massively mistweaked screen. So by all means, try to talk some sense into them and figure out what's acceptable and whatnot.

Mylenium

None of this matters if you are not using color management and even then it's pointless to hang on to web hex colors. If at all you tweak your work to the actual RGB values. Regardless, none of this will improve your situation. Red is a notoriously difficult color for all MPEG encoding and using a fully cranked up red with a slightly bluish hue will never encode correctly due to the chroma undersampling. Point in case: It begins with the design and you need to adjust the colors to be more encoding-friendly and actually fall into color ranges that can be handled.  And then you work in reverse: You create a still frame from the encoded output, not the other way around. You really have things backwards and need to study up on this. You will also need to figure in how the online services re-encode your footage, which may cause further color deviations. There's no academic answer to this and you simply have to experiment and try, but adapting your design to be more MPEG-friendly will likely already go a greeat way toward making things better.

Mylenium