Fair or not, many people make assumptions about you (including your technical and communication abilities) based solely on your email's domain. Since most email domains fall into a few different categories, it's easy to separate them out for comparison:
1.) Your Own Domain -
This is where your email domain typically matches your own website.
These people are professionals. They may or may not be tech-geniuses, but they run a serious business. They have their stuff together, and know what they're doing.
2.) Company Provided Domain -
This is where your email address matches your company's name and/or website.
The vast majority of people won't bat an eye. You're a real estate professional working for a real estate company and have a real estate company's email domain - nothing unusual there.
A small percentage of people, however, may wonder why you would want to tie your email address to the company, thus making it much more difficult to move in the future. Does this maybe give a sense that your aspirations aren't as high as some other Realtors'? And maybe, if you're content to simply "work for the real estate company", you aren't going to work as hard as somebody who is working for himself?
3.) Cable Providers -
These are the email addresses the cable companies give you when you pay for internet access each month.
These email domains give off a less tech-savvy vibe, both because not many tech-type people use them, and because you're putting your livelihood at the mercy of the companies who are notoriously bad at keeping customers happy. Also, you don't always get to take your email with you if/when you move, which may be a cause for lost repeat and referral business down the road.
These domains aren't bad, inherently, but I wouldn't recommend using them to run your real estate business.
4.) Free Providers -
These are the email domains, usually web-based, that you can sign up for, for free, and access your email from any computer that has an internet connection. The popularity of each service has come and gone over the years, although many of the domains keep their email services active even after the domain itself has fallen from grace.
Most of these providers run through a life cycle of "That's a common, popular email address", to "That email address seems a bit outdated, bro", and then eventually to "Dude, your email address is for dinosaurs."
These emails offer great benefits - they are location-independent and job-independent, while also being free. But you'll want to be careful about tying your business to a service which can become outdated over time.
Today, gmail has managed to retain most of its "common, popular" status, and even has a bit of tech-savvy connotations with it. The rest of the list is in various stages of decline, or already dead.
Think I'm crazy? Check out the infographic below, published by the oatmeal: