“In that day.” “That day” is the “day of Yahweh” (see commentary on Zeph. 1:7).
“those who leap over the threshold, who fill the house of their Lord with violence and deceit.” The custom of stepping over the threshold is not well understood. In the time of the Judges the ark of the covenant was captured from Israel by the Philistines, who took it to a temple of Dagon, and because of what happened the priests of Dagon do not step on the threshold of the temple “to this day” (that is, the day when Samuel was written; cp. 1 Sam. 5:5). But how that custom or a custom like it could have come into Israel and been practiced at the time of Josiah is not known.
What can be clearly seen, however, is the hypocrisy of the practice, because the same priests who were careful not to step on the threshold went on to fill God’s house with violence and deceit. Thus they cared about things that made no difference and cared nothing about things that mattered greatly. So 600 years before Christ, the priests were straining out a gnat but swallowing a camel, just as they were at the time of Christ (cp. Matt. 23:34).
“the house of their Lord.” This is God’s Temple.