Given that this claim is patently untrue, it is hard to know where it originated.  It is also difficult to understand how the "experts" who have supported the claim came to such a decision - assuming that they actually bothered to investigate NLP first hand.

According to one web site that carries accurate and useful information about cults (see the Cult Information Centre):

"Every cult can be defined as a group having all of the following five characteristics:

1. It uses psychological coercion to recruit, indoctrinate and retain its members;
    
2. It forms an elitist totalitarian society;
    
3. Its founder leader is self-appointed, dogmatic, messianic, not accountable and has charisma;
    
4. It believes 'the end justifies the means' in order to solicit funds and recruit people;
    
5. Its wealth does not benefit its members or society.

Having investigated a number of cults myself, over a period of more than 10 years, in my opinion this is as good a basic definition of a cult as we are likely to find.
And that being the case, how does NLP measure up as a cult?

1. Does it use psychological coercion to recruit, indoctrinate and retain its members?
    
   Since there is no central organisation to join, clearly people cannot be "recruited" to NLP in the sense that a genuine cult recruits members.  By the same token, since there are no "members" they cannot be "indoctrinated" in order to "retain" them.
    
2. Does it form an elitist totalitarian society?
    
   Whilst it is true that some people may imagine that being trained in NLP-associated techniques makes them superior in some way, this is a misconception and there is nothing vaguely resembling "an elitist totalitarian society" within the field of NLP.
    
3. Does it have a self-appointed founder leader who is dogmatic, messianic, not accountable and has charisma?
    
   Whilst a certain amount of hero worship goes on amongst some sections of the NLP community, since there is/are no overarching organization(s) controlling NLP-related activities, to be strictly accurate, NLP has no "founder", let alone "founder leader," in the sense that it is used in this definition.  Richard Bandler originated what is now known as NLP, and Bandler together with John Grinder were the original co-developers.  Neither of these people, so far as I know, has ever claimed to be a re-incarnation of Jesus or any other "messianic" figure, though some NLP seminar ads have implied that Bandler is to NLP what Mozaert was to piano playing - in a teaching capacity, that is.
    
4. Does it believe that 'the end justifies the means' in order to solicit funds and/or recruit people?
    
   Again, there is no central body so there is no one to "solicit funds" - though naturally companies offering NLP training all charge for their courses, and NLP-related "professional bodies" such as the Professional Guild of NLP charge subscription fees in the same way as professional organisations in any other activity.  There are therefore no "solicited funds" involved.
    
5. Does it accumulate wealth that does not benefit its members or society?
    
   No central organization, no "solicit[ed] funds", so no "wealth."

In short, although there are certainly people involved with NLP who, as in almost any field of human activity, tend to exaggerate the importance and efficacy of the techniques they have learnt about, this is an individual thing and is certainly not inherent within NLP itself..

Just as it would be wise to treat exaggerated claims about the benefits of NLP with a hefty dose of scepticism, it would be equally advisable to disregard the claims of the self-styled experts who, in describing NLP as a cult, only demonstrate that they are ignorant about cults, or NLP, or both.

CAVEAT
Whilst NLP is not itself a cult, it is true that some cults have used and/or are using techniques similar to those used in NLP.  Given that the techniques in question are all in the public domain, and most have been described in numerous books, magazines, etc., it should not supposed that this "sharing" of ideas means that the originators, developers or NLPers in general, encourage or sanction the misuse of any NLP-associated techniques on any person or group for any reason.
The concept of using NLP-associated techniques to produce beneficial, win/win results, has been a generally accepted standard from the earliest days of NLP's development.  Anything else is a violation of the voluntary but widely agreed standards prevalent within the NLP community.