You have to be "out there" as an indie author, easy to find and easy to access. You've got to be on social media and build up your author page, join in on forums and respond to fans who have something to say to you. But there will be lots of times when you don't like what they say. Not everyone's going to be a fan. When those non-fans approach you, and they will, you have to learn how to master a necessary skill: grin and bear it.
Let's Get Critical
The entire world is full of critics, and the Internet allows everyone to get critical about anything that they see. Many, many people choose to exercise this right. Some of them are going to do it with you. Can you handle that?
The Internet allows for a type of communication never before seen. It allows for spacial barriers to fall away, so that two people can have real time conversations even from opposite sides of the globe. It allows for exploration that was never possible before. And it allows for people to act a lot like jerks.
...Not to put too fine a point on it. Some people are going to say all kinds of stuff to you. They will be highly critical. They may even get personal. And that's not even the worst of it. You'll run into all sorts on the Internet, and the more you promote yourself the more exposure you'll get.
That might attract weirdos, for lack of a better word. You may have strange stuff said to you, and I mean really strange. Real celebrities get death threats and crazy invitations all the time. If you're trying to be out in the world and make a name for yourself, the weird stuff comes along with the territory. Usually it's harmless. If you suspect that it is not, you do need to alert the authorities. Most of the time, however, this will not be needed. Most of the time, you're going to have to take even the weird stuff in stride.
As with your critics, you have to learn how to grin and bear it. You have to appear to brush off criticism. You have to remain polite but firm with your potential Internet stalkers. You have to remain accessible, but somehow untouchable.
You have to be a professional. I've given that advice in a lot of different blog posts in a lot of different ways, but it always boils down to the same thing: your behavior must remain constant. You are totally unfazed by negativity and criticism and weird stuff online. You are polite, but you are cool. If someone points out a mistake, thank them. Always thank them for their comments and their advice, no matter what it is. Don't have any other reaction. Do not try to change opinions, make arguments or correct your critics.
Say thank you. And move on. You are an indie author. You are a brand name. Once you're in that zone, you stop being a complete person. You're a product to be sold, and no one is going to buy a product that rants and raves at criticism no matter how ridiculous or inappropriate it may be. Grin and bear it. Stay cool. Stay professional. You can always cry, alone, later on.
Remember: say thank you, and move on.