In a perfect world, safe spaces shouldn't have to exist.
In our world, I can see why in some places it's done as a last resort.
You definitely do run the risk of shielding yourself from dissenting opinions, and that can cause problems later in life when you're placed in a situation where you have no choice but to confront an opposing opinion, and don't know how to correctly handle that situation, but safe spaces as they are used right now are a "we don't have any other option" situation where getting the culture of hate to stop isn't going to happen any time soon, and not everyone has the strength to withstand it day after day in the hopes that one day it'll get better.
I think the problem people have with safe spaces, even if they do not intend to be, is that they do infact form an echo chamber of opinions. And you may see that these opinions as things that are universally true (aka, you're not going to hell for being gay). But there are still going to be some parts of the world that don't see it that way.
And once you leave the wonder and protection of university, where will your safe space be? How prepared are the people who regularly turn to safe spaces to deal with those who disagree with them, even if it's something as insane as thinking you're go to hell just for being yourself?
I get why safe spaces exist, and I lament the reason why they have to exist in the first place, but I wonder long term how well it prepares people to deal with the outside world.
To address your question of where the safe space will be, I think the answer is typically your circle of friends or your chosen family that you spend much of your free time with. I don't think "safe spaces" are really anything new because they typically guarantee that someone is not going to challenge, condemn, or criticize some immutable aspect of yourself. Does anyone have in their circle of friends someone who talks to them in that way? Don't people typically not maintain a friendship with people who make them continually feel "less than"? I'm not talking about political differences like public spending or how public transportation should be developed. I'm talking about not being friends with people who feel they're superior to you. Don't people naturally shape their social circle with that in mind or subconsciously? Furthermore, just as another example, when deciding where to live, I know some people in the United States already consider not wanting to live in certain regions because of the political climate or social beliefs of the area (e.g., "liberal fruity/nutty California," "the backwards South," etc.). I think people naturally already cluster into "safe spaces."
I think the only difference is that now certain amounts of property and private spaces are being dedicated to it in formal ways, while before it was kind of unspoken or labeled differently when it came to who was allowed where. For example, think of birthday parties and weddings. Those invitation lists are doing a weeding process, but it's presented differently as just being "only friends" and then people who were not invited are often kept out and kicked out. But as I alluded to before, who are the people invited? I have to imagine you don't invite a person who condemns or hates you to your birthday party or your wedding (ignoring any crazy family members, of course, who probably aren't going to be at your birthday party and will only be spoken to for 20 seconds at your wedding), so I believe you've just made a makeshift "safe space."
I think the issues you raise are valid if people lived in safe spaces their entire lives and then were suddenly thrust into the world. However, people don't grow up with safe spaces and they don't live 24/7 in safe spaces while attending college/university (classes, bars, dorms, etc.), so I think most people know how to cope once they leave. Plus, they have their friends, just like everyone else, and thus a new safe space to enjoy. Ideally, as I think you alluded to, everyone will be able to enjoy "safe spaces," the kind I'm talking about, everywhere someday.