State extraction is possible with all RNGs to varying extents. These are not stream ciphers. Good seeding remains important always, and that's part of the crypto protocol, not the RNG. This is not a problem for using MT responsibly in things like key generation, etc...
Again: don't sweat this. If you are competent to write your own crypto code and have a good argument for xorshiro or whatever, then use that. If you just need a random number for whatever reason, use your library and don't bother with the advice in the linked article.
Good libraries have more than one random number generator.
Yes, use your library if you are not competent to write your own or don't want to, but use the right library function.
For example don't use random.randint() in Python if you need a random integer for crypto. Use random.SystemRandom().randint(). The former uses Mersenne Twister and is predictable. The latter uses os.urandom() for its underlying random bytes, which uses an OS-specific random source (/dev/urandom on Unix and Unix-like OSes) and should be sufficiently unpredictable for all cryptographic uses.
There is also the secrets library in Python 3.6 and later. It's not better than random.SystemRandom, it's just a different interface to the OS secure random number generator. If you want your code to work unmodified on Python before 3.6 it is fine to use random.SystemRandom (or if you like its interface more).
> For example don't use random.randint() in Python if you need a random integer for crypto.
If you need a random number "for crypto", you should be using a crypto library's key generation function or whatever. What you describe is writing a crypto protocol, and that's way out of the realm of discussion here. (But yes: you don't naively use a PRNG of any type for that. The SystemRandom() utility hooks the OS entropy pool.)
There are situations where the Pyhton random module can provide easy API for cryptographically unpredictable events.
E.g. you can pick random words for passphrase from wordlist with random.SystemRandom().choice(word_list). SystemRandom is a CSPRNG. It's of course incredibly dangerous that you can accidentally use MT by forgetting to put in the SystemRandom() part. random.choice(word_list) works as well and doesn't fail tests.
It would be really important to make all RNGs cryptographically secure unless explicitly stated that the RNG must be very fast at the cost of predictability, and the naming should reflect that, e.g. insecure_scientific_random.randint() for Monte Carlo simulations etc.
Again: don't sweat this. If you are competent to write your own crypto code and have a good argument for xorshiro or whatever, then use that. If you just need a random number for whatever reason, use your library and don't bother with the advice in the linked article.