The Shulchan Aruch specifically mentions in Siman 90 of Orach Chaim that one needs to dress in an honorable manner when one prays. If you appear before a judge, come dressed like a slob, and ignore the judge when your cellphone goes off, he’s not going to be too inclined to listen to you. Rabbeinu Yonah mentions having a clean garment to put on by davening. Hashem is not only our father but our King as well.
That said, this is in regards to oneself. One does not judge other people- “Betzedek tishpot amisecha”. Judge yourself harshly, others favorably. If someone comes to shul dressed that way, let him be. There may be other factors which make his tefilla more accepted than yours, even though he’s in jeans and you’re in the hat and jacket. In a shul I attended in Israel the locals came in a clean white shirt and their best jeans on Shabbos. If that is the minhag hamakom, then one is not making a casual statement by coming to shul in jeans.
Around the house is clearly another story.
Let’s expand the topic- what about coming to shul in shorts or sweatpants?