I don't get it, what's the point of type checking if not to reject invalid programs? The point of a type system isn't simply to add annotations to a programmer (and some type systems can omit them entirely) but to define the subset of programs that are correct within the set of all the programs that can be expressed.
I understand (and have used in production) optionally/gradually typed languages, and without fail codebases will opt for using types up front and not ignoring type check failure because they are always incorrect.
A type error is the compiler/run time telling you "I don't understand what you told me" so why do you want to ignore that?
And if the point is that you want to be able to change the type signature of something without having to refactor giant chunks of code, then that suggests your code is structured poorly to begin with. It should be easy to pull in what you need and play with it without affecting everything else if you haven't done a bad job of architecting the codebase.