でも最近になって、人々は丼ものやラーメンといった、より幅広い日本料理に対しても心を開きつつある。

でも最近になって、人々は丼ものやラーメンといった、より幅広い日本料理に対しても心を開きつつある。but, recently, people is opening their heart even though they face with japanese cuisine which is wider than donburi and ramen.
is my translation from japanese to english correct ?
what's the difference between 最近 and 最近になって ?

Your translation doesn't work as English because of some errors and because the general point of the original Japanese sentence is somehow lost. Let me try to shape it up for you

Recently, people are even opening their hearts/minds to a broader range of Japanese cuisine, including donburi and ramen.

There would be a few ways to say it in English... the above is just an example. The difference between 最近 and 最近になって is insignificant.