No.

If you used const correctly, you couldn't change anything about the class, therefore it was also thread-safe. If your class had mutable members or got around the const guarantee through backdoors (e.g. pointer passed in that modified another object, or member pointers that called non-const methods), it wasn't correctly const and shouldn't have been marked as such.

There is nothing wrong with the const keyword, just with programmers who marked things const that broke the const contract. There is no language ambiguity on this.