I don't know any css, and cannot possibly change that on my own.
There are no any CSS conflicts. It's a js conflict with admin-ajax.php usage.
how can that error make that 5 people can't attach files, while 100 can?
To find the answer to this question we need to know a conflict maker plugin. Probably the plugin has some settings that don't allow some of your users to attach files or something else.
Please deactivate plugins one by one and check after each deactivation to find the problem maker. Let us know the result.