The same banking regulations will apply to this bank. Just as the same food hygiene regulations would apply to McDonald's.
This is a small, commercial bank. Chinese ownership will not be crashing any markets. They aren't in it to crash the bank. They are interested in profits. This acquisition is insignificant in the grand scheme of things.
Many other state-owned banks have been operating in the US for years. Where was the outrage then? China isn't a big scary monster.
That said, I still oppose state owned banks taking over other banks, but it's not big scary news, it's just a continuation of the same system that has been in place for centuries.