There is a schism. As scientific method has opened the external world to wider and wider agreement on how to observe it and what conclusions we should draw, our observations of inner worlds have done the opposite. The work of Foucault in particular addressed the relationship between power and knowledge, and how they are used as a form of social control - it should be noted he didn't accept that there are no external observations, only that we cannot help interpret them, and interpretations have subjective motivations. This led to postmodern anti-foundationalism, more or less a consensus that meaning and purpose are subjective creations.
There are certainly those in the scientific world who think they can make science of everything, but they inevitably build a kind of scientism which mimics the problems of thought and institutions they criticise. Just as people use ideas like Foucault's, beyond their remit to dismiss the idea of any objectivity.
Units are cultural, but what about length? No doubt some tribe can be found that thinks differently about or without it, like those that don't have right and left (everything is referenced to compass points) or see past ahead and future behind them. Semiotics, the study of signs and symbols has to be part of reconciling this. Science, mathematics, do not in truth exist outside of minds in communication with each other that agree on symbols for communication. Yet, not only creative acts, but actual communication of situations and experiences, including arguments and proofs, agreements on systematic methods for observation, then become possible, and patterns of response to shared experiences formalised in concept like length. Cultures with rockets all have formalised ideas about dimensions & rates of change, and will be able to use rockets and other products of that to be more adaptable and exercise power. Literal evolution of ideas.
Variations in 'national character' are a really interesting case. People point to aspects of language, physical conditions like weather, and cultural things like religion institutions and economics. Individuals vary, but we have a strong sense some generalising is valid, and research bears this out for instance notional variations in what aspects of meditation are found difficult. The impact of national character on colouring thinking is hard to distinguish from inside though.. Even what observations are made is shaped by character, meticulousness, optimism, patience, will shape where we look and what we see.
It seems like what there is to see when we do look is 'out there', but we have to accept a creative participatory relationship with that. In that view, accepting that language is a construct of human minds, even when formulated into maths and science, becomes easier to reconcile with, and with the essentially communal endeveaour of developing and refining that (the Private Language argument). We have to look away from the schism, to the interplay between observations and meaning, and to the realities we create together.