That's a nonsense question, because the Constitution doesn't give you the right to use Rackspace's computers in the first place. Rackspace owns them, and has the understandable perception that it's their choice how they get used, not 'rbanffy's.
Counter-example: You own a bookstore located in a mall -- leased space. The mall's managing company says you are no longer allowed to sell Bibles.
Now I'll apply your logic.
"The Constitution doesn't give you the right to use that mall space in the first place. The mall owns it, and has the understandable perception that it's their choice how it gets used, not yours."
Hopefully you can see that something has gone wrong, regardless of legal compliance. Freedom is neither bestowed by a piece of paper nor by men with guns or gavels. It is a cultural trait manifest in our actions. We're not free unless we live like free people.
Would you call yourself a musician if you had no instrument to play? How can you claim to have free speech, if your medium of communication is removed whenever you try to say something unpopular?
Counter-counter-example: you operate a mall and the Ku Klux Klan wants to lease one of your shops.
Note that discrimination because of "race, color, religion, national origin, sex, handicap or familial status" in the sale or rental of real estate is unlawful under the FHA only in the housing market.
What's your point? The issue here isn't whether I think people should or shouldn't be allowed to burn the Koran; it's "what does the 1st Amendment mean?"
The understanding of the 1st amendment is your straw man. By refuting it you believe you successfully refute the argument that this is, in effect, a disturbing form of limitation of free speech by a private corporation who happens to own the machines used to manifest the speech they disagree with.
You absolutely have the right to free speech in the US. But any owner of private property can pretty much ban you from that property, for example (there are certainly some protected exceptions, but in general 'the law' is on their side).
Similarly, Rackspace has the right to stop servicing their customer if they feel the customer has violated the contract. Now, whether or not a court has to step in to determine the validity of the contract, etc, is a completely separate issue.
But this most certainly all has absolutely nothing to do with constitutionally protected speech.
I am not sure the analogies work. It's a Rackspace server on a Rackspace datacenter but nobody is swearing loudly in or carrying weapons into Rackspace's offices.
The weapons being a legal sense. Despite having the legal right to concealed carry, a building can forbid you from bringing it inside.
They are all just cases of someone who is providing a service being able to give stipulations over what can occur there. A church won't let you swear, some places don't want you to concealed carry, and a hosting provider doesn't want you to organize hatred.
In effect, you have your free speech curtailed because you have to express it using someone else's property. Companies like Rackspace may prevent your free speech from reaching anyone for any reason that fits the contract you signed.