Considering other Windows 10 users haven't experienced this problem, it's unique to you. And I don't think diving thru the registry is necessary a good idea. Windows 8.1 has a second Accessibility settings options under the Metro UI, you may want to check there if you haven't.

It would make perfect sense that some accessibility setting would be preventing you from pressing both mouse buttons 1 & 2 at the same since this is not how the mouse is normally used, and could possible be interpreted as an accidental button press. I am not sure why or how this is only happening to you though.