Email sent from my iCloud email has started going to everyone’s Junk I have a username@me.com email address that I've had since around 2011. All of a sudden, about two weeks ago, I've stopped getting replies from people.

Turns out that my emails—including responses to an already-ongoing thread—are ending up in people’s SPAM and Junk folders. 

Why is this happening and how can I stop it? It's a huge problem.
There's nothing you can do, except use a different email address.

What happened, most likely, is that some nitwit spammed from his/her me.com address (or spoofed it), and one of the commonly used spam blacklists added the entire domain. The other people will need to catch this and add your email to their personal whitelist, the details of which will depend entirely on their email provider and/or email software (depending on which one's actually doing the filtering).