Styles vary considerably based on subculture and region. If you would go on a job interview without a jacket and tie, or go to meet President Trump dressed that way – then its probably okay to go to shul without a jacket and tie. Note that many hareidim don’t wear a tie – which in other circles is a sign of disrespect. In the past men often wore a fedora on Shabbos, even though it was a “working week” hat, at least among the better dressed upper crust people. And in many countries, the rabbanim didn’t wear a jacket (particularly in non-European areas). Another factor is local custom of wearing a tallis (since a tallis, which originally was worn as outwear similar to a jacket, makes what is underneath less significant).
The only halacha is one should wear your best clothes to shul on Shabbos and Yuntuf, and that is not an absolute standard.