Mersenne Twister is not cryptographically secure. (MT is based on a linear recursion. Any pseudorandom number sequence generated by a linear recursion is insecure, since from sufficiently long subsequence of the outputs, one can predict the rest of the outputs.)
To make it secure, you need to use some Secure Hashing Algorithm with MT. For example, you may gather every eight words of outputs, and compress them into one word (thus the length of the output sequence is 1/8 of the original one).
It is meaningful to replace linear generators like LFSR with MT.2002-version can receive an array of integer as a seed, and it fits to this usage.