According to the Binance article that I read about it through the twitter link that you posted above, not only USDC, but USDC, USDP and TUSD.
According to the Binance article, people will still be able to deposit and withdraw in USDC, USDP and TUSD. But for trading, it would be automatically converted to BUSD on Binance. But if you deposit USDC, USDP and TUSD, you will be able to withdraw in the respective coins.
I hate this about Binance that is looking for all means to make sure BUSD dominates the stable coin by all means,
This is just the way business works, it may seem unfair but it is obvious that binance is going to want people to use their own stable coin instead of the other ones you can find in the market, and while they cannot force you to do so they can at least guide you in that direction.
So if someone doesn't really like the move they can always leave the binance exchange behind and use another platform which allows them to use the stable coin they want, but I doubt many traders or investors are going to leave binance over something like this, and it is likely that binance thinks the same, which is why they have pulled off this move.