I'm not sure I'd agree that a brand new set of operators is necessarily easier to read than the template solution; particularly if you start to stack up more complex or compound uses. To borrow a suggestion which has already been given to you, consider

if(matcher(Alpha).is_none_of(Beta,Gamma,Delta) && matcher(Alpha).is_any_of(Epsilon,Zeta,Eta) && matcher(Theta).is_any_of(.....) && ...)

vs

if(Alpha [!] Beta, Gamma, Delta && Alpha[^] Epsilon, Zeta, Eta && Theta [^] ... && ....)

I'd argue cognitive load goes up from needing to track the three-character symbols and their relative positions between a bunch of names (especially consider if the names themselves become compounded names or function calls); over a more traditional function call syntax. It adds more characters, yes, but verbosity is not a dirty word if it means making the code clearer. I will agree that the need to insert a wrapping "matcher" template is unideal, but that's how the language works; and adding something as extraordinarily fundamental as a new set of operators to the language requires an extraordinary motivation which in the nicest possible way I don't quite see here. 

How do you propose to construct these operators? Is [!] an operator all its own, or do the commas between terms factor in for a variable number of commas to be possibly attached to the name/definition of each of your four operators? Is A [!] B strictly equivalent to A != B or is there enough difference in how they work internally that you can't make that guarantee? I assume these aren't overloadable operators and you have a reasonable idea of details like precedence figured out - have you looked at how it would interact with the existing standard in terms of wording; including all the various fringe cases and bits that adding new operators and conditionals will have when pathologically arranged? I dread to think how many places the standard refers to operators and constructs which can be treated as conditionals and predicates, so there may well be wording awkwardness aplenty.

Kind regards,
Matthew Taylor