I have never encountered Adblock Plus interfering with Yahoo/Yahoo Mail but NoScript can and has in my situation. I was trying to disable their stupid in-browser Messenger that would pop-up from spammers, when I did disable the related script (yimg.com), it would also stop displaying emails.
I worked around it by blocking the messages through Options > Messenger Options > Privacy which resolved the issue.
Since you already know how to get to the settings, just make sure they are not configured too aggressively like the screenshot below (also if you have any custom filters, that might do it too):