Learn English – Word for who professes discrimination based on culture

Bigotry (“Intolerance or prejudice, especially religious or racial; discrimination (against); the characteristic qualities of a bigot”), is a term commonly used for such a “thought process”. Also note the definitions of intolerance: “Not tolerant; close-minded about new or different ideas. indisposed to tolerate contrary opinions or beliefs; impatient of dissent or opposition; denying or refusing the right of private opinion or choice in others; inclined to persecute or suppress dissent” and prejudice: “An adverse judgement or opinion formed beforehand or without knowledge of the facts” and “Any preconceived opinion or feeling, whether positive or negative” and “An irrational hostile attitude, fear or hatred towards a particular group, race or religion”.

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Wiktionary and Collins English Dictionary define the term handism.

From Wiktionary:

1. (rare) prejudice or bias based on whether a person is left-handed or right-handed  

   • 1993, Stanley Coren, The left-hander syndrome
   Here again the right hand is salvation and the left hand damnation. Contemporary Islamic countries are an interesting example of how handism, as expressed in religious traditions, can also influence more secular activities.

From Collins English Dictionary:

discriminination against people on the grounds of whether they are left-handed or right-handed

As noted, this term is extremely rare.