Let's first take a look at the agencies who probably won't represent you. These are mostly going to be the major agencies (no surprise there) like CAA, WME, UTA, and ICM. These agencies have a high overhead (expensive offices, many agents, assistants, etc.) and need to rep people who are going to hit the ground running as far as booking roles. Not only do they mostly take on union actors, but union actors with strong résumés.
Are there any exceptions to this? Maybe. There are exceptions to every “rule” in show business, but they're very rare when it comes to the big guys. The exceptions for a major agency to take you on with no union affiliation and a soft résumé is if you are making a big splash in new media (like you have a few hundred thousand subscribers on your YouTube or Funny Or Die channels). This is especially true if your videos contain something that can translate into a mainstream performance (like sketch comedy, your own music, stand-up comedy, or hosting your own vlog). The other exception is if you have a lead role in a very hot new indie film that's getting a lot of attention.
Now let's take a look at agencies where you stand a better chance of getting representation. If you're non-union, but have a decent résumé, you'll want to submit to the boutique agencies. These are the small and mid-sized agencies.
Note: Don't call them and ask if they accept submissions from non-union actors. Most agencies don't like phone calls from actors they don't represent, and even if they do talk to you, they will probably tell you that they don't take on non-union actors. But here's the secret – many of them do!
So, why do they say they don't rep non-union? Two reasons – first, they don't want even more submissions then they already get every week, and second, because some agencies think that representing non-union actors lakes them look less professional. So, just send in your headshot and résumé like everyone else and see if they call you in.
And here's the reason why they do take on a few non-union actors – there are some fairly high-paying non-union gigs out there. Especially for commercials (and occasional print work). And although I no longer do non-union jobs, here are two examples I know about from my own experience:
An industrial film for a theme park, that was shooting in Florida. First-class plane tickets, nice hotel, all meals, and $5,000 dollars for 3 days work).
The second one was a commercial for an electronics company in Japan. First class air, a hotel in Tokyo for 5 days, meals, and $10,000!
So, you can see why smaller agencies would want to have a few good non-union actors in their files that they can submit for those kinds of jobs.
Let me know if I can answer a question for you. I know it can be confusing sometimes (believe me – I was totally confused about the business before I got a bunch of experience).