Is reusing keys for CBC and CBC-MAC secure when using encrypt-then-MAC? I know reusing keys is a bad idea, especially for CBC and CBC-MAC, but the example for why on Wikipedia seemed to use encrypt-and-MAC. It seems obvious that the last block of encryption will be equal to the MAC when used in this way.

If it's instead used in encrypt-then-MAC, wouldn't that be acceptable? Every bit of the MAC would rely on every bit of the ciphertext, preventing chosen ciphertext attacks.

Is there something I missed here?
No, it is not necessarily secure. Here is a simplified example of why not.

Assume one block zero messages are encrypted without padding. The ciphertext is $I||E(I \oplus 0)$. The MAC value is thus $E(E(I) \oplus E(I)) = E(0)$. So regardless of the IV, the MAC is the same for all such messages. So if you encrypt several zero messages you can leak that fact through the MAC.

When you take padding into account this exact issue is no longer possible, but you should see how it is possible for the MAC and encryption functions to end up using the same values.