The hard part about being judged is that real bias does part of the job of keeping you down, and then fear of being judged does the rest. It's unfortunate, though understandable.
While there are some jobs for which they can't/won't hire a felon, that's not true of many professional jobs. And from my perspective (and I've hired a fair number of people), someone who committed crimes at age 16, did their time, and kept their nose clean for 20 years...that would actually count for, not against, that person. Not the crime itself, but overcoming hardship, pulling oneself up out of difficult circumstances--that shows a strength of character that someone with an easy life hasn't had the chance to demonstrate. It's admirable.
How you talk about it would matter to me a great deal, though. I'd want to hear you take responsibility for your actions, talk about having repaid your debt to society, talk about what you learned, talk about having built a better life for yourself and wanting to build an even better one and with some passion and conviction.
I do some volunteer work with a local organization that helps chronically under-employed people (usually men, usually from a long-line of chronically underemployed men, often with criminal records, drug convictions, etc.) find work that will support them and their families. They go through training, and sometimes the most important part of the training is getting them to believe they deserve better and that others think they do, too. I do mock interviews, and sometimes they walk in with such an air of defeat, it's palpable, and becomes a self-fulfilling prophecy. And sometimes they walk in full of bravado and excuses about why none of it was their fault, and I don't want to hire those people either. But when they come in with the right blend of humility and commitment to a better life for themselves, I want to do anything I can to give them an opportunity to succeed.
I say go for it, just be smart about it and take on as little debt as you can. Ask for as much advice as you can from people who have the kinds of jobs you want, and actually listen to them.