I can think of three ways to provide for that:
1. Public servers, possibly sponsored by the govt
2. Regulation of Internet access run by private companies
3. Waiting for private competition to create such a space
The first one worked well in the early days of the Internet. There were lots of rules against commercial use of publicly-funded computers but little content regulation. Despite what some may think about the govt, it has lost most times it has attempted to limit free speech.
Regulation sort of works for railroads and telecom lines. Bell gets a monopoly on wiring but they have to provide access to disabled people, can't do discriminatory pricing, etc.
The last one is least likely to succeed. I don't know of any private US company that advertises themselves as "no takedown unless required by court order". It seems there is little profit advantage in marginalized speech compared to the cost of defending against attacks on it.
While it's good to see Ipredator and BayImg providing services with this kind of guarantee, the fact that such an effort only seems possible in Sweden should give us pause.
How far can you bend your constitution before it breaks?