I do consulting for bars and restaurants. I work directly with clients about 1/3 of the time, the rest I spend running the entire business in my region.
I came out to two of my coworkers first, because we'd been friends for a while. They were both cool with it and didn't think I'd have any issues. I told my boss, he was cool with it and he told the rest of the team and the other locations/corporate office. No issues with anybody. We have offices throughout North America, Australia, and the UK and we employ somewhere around 150 people. No internal problems whatsoever. Everyone has been very respectful and supportive. The office closest to where I had my top surgery even sent food to my hotel room after surgery.
I had to come out to my personal clients as well as everyone else's because I have such a central role in the business operations. I was worried that people wouldn't take it well and would leave. My salary is directly tied to my region's billing. If people leave and billing takes a dip, I either have to fire someone, take a pay cut, or find a new job. And I wasn't about to fire somebody else if I was the cause of the issue.
Fortunately it never came to that. Everybody took it well. I just wrote a blurb in each client's weekly report that I was changing my name, email address, and would be taking some time off in the near future for medical reasons. Didn't need to go any further in depth than that. We didn't lose any clients. Like Dena said, if you do good work, you really don't have anything to worry about. The quality of what you can provide people with doesn't change whether you're male or female or something else entirely, and a good client will realize that.