In english, taboo language may be realized as swear words--though I could see some languages not having "swear words" in the english sense, while maintaining "vulgar expressions". All cultures have taboos. However, do all cultures have linguistic taboos?
First, there's no clear dividing line between culture and language when it comes to idiomatics and usage rules (as opposed to say phonology). So how do we determine that if a culture has a taboo, that it's not linguistic or does not have a linguistic component?
Second, how do you know that 'all cultures have taboos'? It sounds like a reasonable assumption but so was that all cultures have creation myths or all cultures have religions. The first one has been disproven and the second one is debated because of the lack of clarity over what is religion when you don't start from a Christian perspective. China, India, Japan, certain Amazonian tribes all have things that may look like religions but they are not very similar to the traditions that gave rise to the concept in the first place.
Equally, it's not clear what a taboo is. The original concept came from certain religious prohibitions but has since been extended to things like what one does not do in polity society. While it is extremely likely, that all cultures have the latter, it is not clear that they have the former.
In summary, I suspect that all languages have things that are proscribed in certain contexts. And that these exist at the intersection of language and culture. But without a clear definition of what you're talking about when you say 'taboo' and an extensive survey of a large sample of languages, you cannot really answer this question. Given the difficulty of what formulating the question, I doubt it's worth going to the trouble of trying to come up with an answer.
There is something like that in Berber, see: Destaing, E., « Interdiction de vocabulaire en berbère», Mélanges René Basset, Paris, Leroux, 1925, p.177-277. You can read it here: https://www.scribd.com/document/114584799/Interdiction-de-vocabulaire-en-berbere-E-Destaing