You are free to believe that...

Often when I am talking to conspiracy types and I present the evidence and logic for a particular explanation of something they think is a hoax (spacecraft launching satellites for example) they reply with:

'You are free to believe that, I won't judge you.'

Or something along those lines. It's sometimes preceded by a strawman exaggeration of my position to make it sound absurd, but not always. This really irritates me as I know very well what I am free to do or not do, and it really doesn't matter if they do judge me, who even cares in the end and what does it have to do with the discussion anyway?

I'm not sure if it's a fallacy, perhaps a backhanded type of ad hominem? Or a type of poisoning the well against the position I'm presenting evidence for, i.e. the idea is absurd and no one with any sense would believe it, and normally you would be judged as a fool for believing it but I won't judge you (indicating their non-judgement would be an exception to a rule)?

Anyway, I wanted to ask the members here what they think of this type of language, what fallacy it might fall under, its place in a debate or discussion and perhaps some insight into the psychology of the people who use it.

It’s known as a Semantic Stop Sign, thought- stopper, or best described as a thought-terminating cliche (See Robert Jay Lifton’s Thought Reform and the Psychology of Totalism).

It’s not really a fallacy because there’s no deception involved and there’s some validity to it. However, when it is used to quash debate, argument or disputation and quickly devolves into the end of thoughtful exchange it’s pretty clear you’re not really dealIng with a good faith actor.

As mchasewalker correctly points out, it's a thought-terminating cliché - a usually generic, feel-good statement that is intended to stop thought in a certain direction or about a topic. "You're welcome to believe that" is one example of these clichés, where the person retreats into subjectivity by suggesting a well-documented phenomenon is just a 'matter of opinion', so their incorrect view can't be scrutinised and falsified (but they'll still assert it as obviously true, of course). Another example:

Jordan:  "If what X is true, then we should see outcome Y - but we don't see it. So how can it be true?"

Jennifer:  "Stop invalidating people's experiences. It's not for you to question what someone else went through."

Jordan is asking pointed questions regarding the validity of the phenomenon supposedly observed. Jennifer is trying to kill the conversation - and stop critical thought - by suggesting it's not for him to question said phenomenon.

It's not a fallacy because it isn't an argument; it's avoiding making an argument. But it is problematic in other ways, as our members have discussed earlier in this thread.

It's not a fallacy but this attitude is really frustrating. What I would best describe that as "an attempt to reduce truth into just a controversial opinion" (unfortunately I don't have a fancy name for it).
Implying that what you say is not something well-proven and logical and therefore inserting doubt. 
Also the sneaky way they say it is condescending and also bragging about how forbearing they are towards a fool like you who although he's saying stupid things, they will be kind towards him regardless of his stupidity - which is, again, utterly condescending, and also since it implies that you are stupid to believe that but they say they won't judge you (something they already did), it's also passive-aggressive. I think you should watch also this video where the same condescending attitude can be expressed with other phrases filled with covert messages.  
(here it mentions a very similar phrase which is "Ok, if that's what you wanna think")
12 Phrases Emotionally Intelligent People Don't Use

Anyone is free to believe whatever they choose to believe, no permission is required.  People who believe hoaxes are quite sure they know the truth about a topic.  And they do.  Truth is in the mind of the beholder.  You can manufacture your own truth.  You simply cannot question a true believer's truth.  People sworn to tell the truth in court may then proceed to give quite faulty testimony, but in their mind's eye, it is the absolute truth.  People too often confuse "truth" with "fact".  Almost nothing about what a true believer thinks about a hoax is remotely related to facts.  They choose to cobble together a distorted reality based on carefully selected facts relating to an event.  Any facts that don't support their conclusion are ignored or denied.  Most people who originate hoaxes are fabricating an account of an event that will best support their already formed conclusion.  And most people who believe publicized hoaxes readily believe the distorted facts, and seldom do any research on their own. 

It's no surprise that some of the most fantastic hoax theories (such as the faked moon landing) are originated by rather intelligent people.   Bill Kaysing is credited with being the father of the moon landing hoax theory.  He was a technical writer and archivist for Rocketdyne, the company who built the Apollo spacecraft.  His knowledge on the space program was quite extensive.  So when he announced the moon landing was faked, who could offhandedly doubt him?  Only others who worked in the aerospace industry.  And in the beginning no one did.  So other gullible, less knowledgeable people started thinking that since no one was challenging him, he must be telling the truth.  If anyone had bothered to check Mr. Kaysing's training and experience they would have found that he was in no way qualified to make announcements on rocketry capabilities.  And almost all of his hoax theory is based in inference and opinion, not true facts.  Moon landing fake hoaxes have become something of a cottage industry, despite the fact that almost no one cares about it any more.

The point is, Mr. Kaysing was undoubtedly beginning to get some traction from his hoax theory and make a living from it.  He undoubtedly knew it was based on inferences and misunderstood images, but he didn't care, as long as he was getting attention.  After awhile his hoax theory did what all hoax theories eventually do when allowed to continue unchecked - it gathered momentum and gained enormous public support.  Roughly 12% of Americans currently believe the moon landing was faked.  But something else his theory also did.  It became his "truth".  After repeating a lie long enough and loud enough, he came to believe it was true.  And so it was - to him.