I’m sorry Erwin, but web designers not looking for ‘Generic RGB’, there is no such thing and everything will go badly wrong if you attempt to work with it. sRGB is a fact, a defined colour space that has been ubiquitous for consumer devices for the last 20 years.
For web design, everything should be setup as sRGB. However, your problems are arising because an Apple display has its own colour profile, so a screen grab for example has to be opened in Photoshop and ‘Converted’ to sRGB (not assigned as) before use in a proper colour managed environment.
To get accurate hex vales for a graphic, open it in Photoshop / Illustrator or similar. These applications will read the colour profile and as long as colour space is set to sRGB, the graphic will be displayed correctly and the picked hex values will be correct in RW. I spent years working with this stuff in the noughties and ended up setting up colour management for Reuters, Globally.