Both sentences are grammatically correct and semantically equal. However, semantically I'd call both sentences (equally) wrong.
In general
The keyword here is the term Nachfeld.
The grammatical information system of the IDS (Leibniz Institute for the German Language) says:
Das Nachfeld kann in allen drei Verbstellungstypen [...] besetzt sein, muss aber prinzipiell in keinem realisiert sein: Im Unterschied zum Vorfeld in Verbzweitsätzen gilt das Nachfeld prinzipiell als strukturell fakultative Position. Das Nachfeld kann sowohl Hintergrund- als auch Vordergrund-Informationen enthalten[...]
The IDS lists several examples, one of which is:
Für ein paar Stunden ist der Präsident der Bundesbank zurückgekehrt in sein altes Leben. (Die Zeit, 25.10.2009)
Of course would "Für ein paar Stunden ist der Präsident der Bundesbank in sein altes Leben zurückgekehrt." also be correct.
So this is just one more degree of freedom in German language. But although the first of your given examples is as grammatically correct as the second and similar examples are widely spread (not only in colloquial language, but also in proofread newspapers and books), there are some people, even native speakers, for whom such a word order sounds unfamiliar.
This case
In your given example I see a semantic error: The cork footbed is not famous for the shoes. The shoes are famous for the cork footbed. However, it might be a philosophical question whether the shoes made the cork footbed famous or the footbed made the shoes famous.
In order to rescue the question about the word order, we could modify the sentences a bit:
Er erfand das Kork-Fußbett, das typisch ist für Birkenstock-Sandalen.
and
Er erfand das Kork-Fußbett, das für Birkenstock-Sandalen typisch ist.
I guess, both sentences are correct (although they are far away from being elegant).
However, simpler and more usual would be
Er erfand das Kork-Fußbett, für das die Birkenstock-Sandalen heute berühmt sind.