Proponents of linguistic relativity (or "Whorfianism") have come up with some fantastically absurd claims over the years about how thoughts are constrained by language. And in the popular imagination, these claims would inevitably entangle with stereotypes about speakers of different languages. So I don't blame people for dismissing any discussion about the relationship between language and cognition as fringe theory…
What you say about how language does not constrain our thoughts is borne out by American English. This was the product of Noah Webster and his educational materials including the dictionary - 'Mirriam Webster'. The rationale was to move the language away from 'aristocratic' English and to make things secular. Obviously the spellings survived - 'color' - but god somehow thrived in America (we are secular in the UK). W…
Any influence he might have had was in matters of diction in the sense of vocabulary and stylistic choices. If Webster's educational materials were intended to be secular, they achieved this by choosing expressions that avoid religious references, for example, not by changing the building blocks of the language to make secular thoughts easier to express. The relationship between diction and cognition may be an interesting topic in itself, but it's not what we mean when we usually discuss language and cognition, where we are concerned with the structural aspects of the language itself, e.g. its tense or pronoun system, not the stylistic choice of what we express with it.