If you read the parable you'll see that the "choosing" is done at the end.
The one who was thrown out of the banquet was invited along with everyone else, but showed up wearing dirty clothes. Both clean and dirty clothing are recurring analogies in the new testament. When a person is baptized he is considered clean, and wears "white raiment". To dirty ones clothes is to sin afterwards:
Rev 3:4 - ‘But you have a few people in Sardis who have not soiled their garments; and they will walk with Me in white, for they are worthy.
Those of Sardis who had soiled their garments through sin will be cast out at the end, but the righteous will continue to walk in white.
So no, Matthew 22 doesn't do much for Calvinism.