[Paraphrase] Is there a secure MTP stream cipher?
I would argue that there isn't, at least, not with a reasonable interpretation of "MTP stream cipher".
For "MTP stream cipher", I will put on two constraints:
It is deterministic [1]; that is, there is no IV or other randomizer, and the cipherstate is not updated between messages. Obviously, there exist ciphers that either use an IV or update the cipherstate; however if you do that, you can easily generate different keystreams based on the IV/cipherstate, and so I would argue that those are not 'MTP' ciphers
It is online; that is, when generating a section of ciphertext, it takes a section of plaintext and the current cipherstate, and generates that part of the ciphertext (and possibly updates the cipherstate). Specifically, that section of the ciphertext is not affected by later parts of the plaintext. I would argue that if you have something that violates that, it is not meaningfully a 'stream cipher'.
If we have a cipher that abides by both of the above constraints, consider what it would do if it were given the two plaintexts:
$$AAAA...AAA$$
$$AAAA...AAB$$
For the first part of the ciphertext, it must generate identical ciphertexts for both messages; because the plaintext it is allowed to see is identical, and because it must be determanistic. Hence, the fact that the two plaintexts are related is obvious from the resulting ciphertext, hence it is not secure.
Hence, to achieve security, any cipher must break one of the two constraints.
[1]: One might claim that determinism automatically rules out security, because an adversary can distinguish a deterministic cipher from random by requesting the encryption of two identical plaintexts. I won't do that here; it is not that unreasonable to relax the CPA constraints to require the adversary to choose distinct plaintexts, especially when realing with a real world application that has the constraint that ciphertext size must be the same as the plaintext size.
