Just for clarification regarding Actor's Equity CMs. I know there's been some confusion surrounding which roles are AE, what that means for shows and characters in the parks. Not all face characters or Character Performers (any CM portraying a character in any way) are AE -- in fact, most are not.
To be an AE CM, you must
not only be portraying a character (doesn't have to be a famous Disney character, it could just be a Hollywood director from the '30s for example

) but also
performing some sort of speciality skill at the same time. It's that specialty skill or talent that distinguishes the AE CMs from other Entertainment CMs. This might include singing, advanced choreography, improv/stand-up comedy, or "stunts" (acts like what you see IJESS or in FoTLK). A speciality skill could also be something like puppeteering, which you see in Finding Nemo: The Musical. Advanced Acting is even considered a specialty skill (albeit with strict rules) if the Actor has to portray the character but also recite a certain amount of memorized, scripted lines at the same time. Basically, if the skill requires extensive, individualized training that cannot be easily obtained with TWDC (in other words, you have to study it), it's likely considered a specialty skill. That mix is what makes a CM "Equity" and there are very strict rules as to what Disney can and cannot do with those rules.
What are some other AE CM roles? As alluded to, Streetmosphere characters (like Citizens of Hollywood) are AE CMs. The comedian(s) portraying each of the live interactive monsters at MILF is/are also AE CMs. BatB also uses AE CMs, given the advanced choreography and acting/reciting memorized lines required in each performance. So yes, a face character
can be in AE, but portraying a character doesn't automatically get you in. You have to do something else "special." You don't necessarily even have to be performing in a theme park. The BW entertainers were all AE at one point (I *think* they still are).
One common point of confusion: parade characters (such as those in FoF or any of the cavalcades) are not AE, because they're usually only portraying a character. There's no extensive "acting" (usually any character audio is pre-recorded) and most of the dancing is done by background dancers not portraying any character and those routines generally do not fall under the classification of "advanced choreography" anyways. The dances are actually surprisingly easy to learn (take it from a guy with two left feet who still learned the MISI dance from a friend who performs in it).
ETA: Before these two questions come up: JC Skippers are NOT Actor's Equity. First of all, they're not (at least supposed to be) improvising or be stand-up comics. They're supposed to recite from a script with several options for each scene. That script is written in a way that brings it below AE's requirements for advanced acting/lengthy memorization. They're also Attractions CM (because they operate the attraction), not Entertainment CMs. Skippers are actually quite limited in what they can and can't say and what they can and can't do. That doesn't mean that some don't bend the rules (and they take a risk when doing it), but theoretically a Skipper with tons of acting/performance experience should be just as good as a Skipper with zero acting/performance training. All of the "spiel training" is done in house (as part of On the Job Training for any new Skipper). After all, public speaking is technically not the same as performing/acting.
Second question: when are the AE shows coming back? Our favorite word: soon. Supposedly, they're trying to get them all back up before/around/or shortly after (heard all three) Labor Day.