Chomskyan theory is less dominant than it used to be. Before WWII, linguistics was largely the study of European languages, and as a result, there seemed to be a lot of similarity between languages. Chomsky was on the tail end of this.
In recent years, the amount of research of non-European languages has exploded and we've realized that languages are much more diverse than we thought. For example, it's not just a matter of SVO, OVS, VOS, or any permutation of the previous; some languages don't even use the subject-object pattern(they do something called ergativity).
TLDR: there may be some sort of innate grammar, but it is much, much more murky than we used to think.
In recent years, the amount of research of non-European languages has exploded and we've realized that languages are much more diverse than we thought. For example, it's not just a matter of SVO, OVS, VOS, or any permutation of the previous; some languages don't even use the subject-object pattern(they do something called ergativity).
TLDR: there may be some sort of innate grammar, but it is much, much more murky than we used to think.