So I've actually seen this same issue with IndustrialCraft - More Qualities (1.0.5) and I could not fix it by adding my own dependency to Quality Effects' info.json to make Quality Effects load later.
It looks like the issue is More Qualities doesn't insert their new qualities during the "data" phase, it waits until the "data-updates" phase of load. Since Quality Effects scans the qualities and makes prototypes during the "data" phase (e.g. before More Qualities has added their new ones), it doesn't know the other qualities exist and crashes the game when it tries to reference them.
The easy solution is to open the .zip and rename the "data.lua" file to "data-updates.lua" as well as adding the line "? ic-more-qualities >= 1.0.0" to the "dependencies" section of the "info.json" file. I have confirmed that this fixes this particular issue.