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.
But once you move away from the deterministic end of the spectrum, it is clear that there is some relationship after all between language and thought. The key point to understand is, as the linguist Roman Jakobson put it, that “languages differ essentially in what they _must_ convey and not in what they _may_ convey.”
An oft-repeated trope is that if a language does not have a word for some concept, then its speaker cannot understand this concept. This is plainly rubbish. Language does not constrain thought in that way. People can understand concepts without having the words to express them, and if need be, can always find new ways to express them in words, coining new terms if necessary.
Reality is much more subtle. Language only determines what we have to pay attention to. Take a look at the example of the distinction between cups and glasses in English as opposed to that between "chashka" and "stakan" in Russian. Suppose a Russian-English bilingual was presented with four objects—a cup-"chashka", a glass-"chashka", a cup-"stakan", and a glass-"stakan"—and instructed to group them into pairs of similar objects. What would the response be? Would it depend on the language that the instruction was given in? These are the sorts of interesting questions that we can ask about language and cognition. Speakers of different languages are capable of performing all the same cognitive tasks, but different languages may privilege different pathways to the solution.