The term "puritanical" doesn't exclusively refer to the existence of or adherence to the Puritan religion, and when it does, the term is usually capitalized. From Dictionary.com:

    puritanical [pyoor-i-tan-i-kuhl] adjective

    1) very strict in moral or religious matters, often excessively so; rigidly austere.
    
    2) Sometimes Puritanical. of, relating to, or characteristic of Puritans or Puritanism.

It is entirely possible within the parameters of commonly understood English parlance for Muslims, or any group, to be puritanical.

my culture says pedophilia and murder are ok and you should respect my culture.