obviously not a lawyer either,
but my take on the whole contract vs free speech, would involve the inevitable question what is a contract/agreement, what really is free 'speech' to my understanding it its not the literal sounds escaping your mouth, is the ability to formulate, and convey a message.
does your speech have liability? etc. the classic yell fire in a movie theatre debate, is it really a crime that you yelled fire, or if you had intended to cause panic/riot/a scene, if you were to have a satire skit about a famous person committing some heinous crime that could potentially be fine, but if you say possibly the exact same phrase but with a different context/tone that you are not joking, the pretext being your trying to say they actually did this would be libel. as its the actual message intended to be conveyed not the literal text most of the time, in my opinion.
but basically.. if it had been established that you could have repercussions from your 'speech', i could see a possibility for an argument such as that an argument or 'promise' as https://www.law.cornell.edu/wex/contract sort of describes, is an act of speech. and thereby possibly fall under the same level of liability
for the mall thing, might be more complicated in that.. some malls may be built with taxpayer money and with zoning whatever stuff commercial versus say a regular house, might imply other things. and that in a place like a mall could be that its just considered to be public because they lease out the shops. complicated in much the way if someone was to complain you said a bad word walking down the hall of an apartment complex which you held a lease. in that.. a vendor might be able to eject people from the store for a different policy than a different vendor. that say.. the mall of america which has planned construction stuff, where theres going to be hotel and nightclub space, if people are drunk there, inside the mall, what does that mean for their policy on people being drunk in random commons, or in a store.
basically.. they may have provisions for a per vendor/per type of area basis or something, besides potential local or state variances/zoning whatever stuff. but there could be an alternative argument that if you present yourself as a public space, and the public/community as a whole considers you to be.. at what point are you?
which could go into the same liability of statements that you make, in that if you say anyone is welcome but enact a policy which is otherwise, you might have to deal with flack about it in the public, or in some cases like.. the gay cake whatever stuff it might even be enforced that you have to stand by it.
which could bring other arguments into it.. if your business is acting on a policy which the public defines as indecent. such as if a mall had stated 'no public displays of affection by gays' meaning cant even hold hands or something could go bad for the mall ownership, where sex acts would probably go bad for the people involved
but as far as personal opinion.. if i had to guess, id say an agreement can affect your ability to speech, or rather your ability to use a service/claim access to something; the other parties liability to let you say those things or use their services could be limited if its like an actual agreement that is well defined and obvious that you are 1 agreeing, and 2 the things in question and liabilities involed etc.
basically that you arent just saying, oh your using the site therefore you agree with all goings on of the staff, without having ever had it stated to you that you are agreeing to that by clicking continue or whatever, i wouldnt see standing probably
tldr cool