No. This is a free speech issue. Those who feel offended are also free to burn bibles and desecrate whatever they feel proper.
As much as we disagree with the book burning festival (it is a stupid thing to do and there are much more articulate ways to express disagreement with Islam), I find freedom of speech is a much more important issue than the sensitivities of religious groups.
I was actually a part of making this happen for someone who called in -- I had a high voice at the time, got called "ma'am" a lot. A male customer was coming on to me, wanted to send me flowers. As I was trying to assist them, I noticed the call records - some employee codes I recognized as males had notes like "lost call" and "customer hung up"; females had notes like "customer made inappropriate comments". Long story short, a supervisor listened in, and after they made sexual advances and used profanity, got their telephone service cut off (and I don't just mean long distance, I mean local service - the LECs in those days still had a good relationship with AT&T)...
So where's the right of free speech there?
Still not quite the same issue, because that involved federal law, whereas this is regarding Rackspace contracts... But it's an example of something trumping free speech.
The shorter and more classic example is the [lack of] right to shout "Fire!" in a crowded theatre [when there is no fire].
This is nothing like shouting "fire" in a crowded theater. It's not also profanity or improper conduct in a one-to-one conversation.
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?
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?"
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.
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.
It's important
You have the right to free speech, but you're probably going to be quickly ordered to leave a church if you begin swearing loudly.
You have the right to bear arms, but buildings are free to forbid you bring in weapons of any sort.
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.
Except, possibly, finding an ISP whose TOS are more tolerant of customer content. I'm sure they exist, I just wouldn't know where to find them.