Can anyone suggest a streaming movie service that has a selection comparable to Netfix and will run on a computer using GNU/Linux?
No. There isn't one because Linux market share on desktop is so incredibly small that no one wants to put up with the cost of supporting those few users. Most normal people run either Windows, set-top box or some console like PS3. Even if someone were to make such service they would immediately get huge backslash for the need of DRM (demanded by copyright owners). Yes, continue to use Linux, I do too. But if you are not willing to come even a little bit forward (like, accepting DRM or closed binaries) don't cry about it when companies don't want to support it.
"It may be that our role on this planet is not to worship God but to create him." -Arthur C. Clarke