What the Bible says about Thank Offering
(From Forerunner Commentary)
This shows that feasting on the new moons was not looked upon as something unusual but expected as a matter of social custom. It was not evil nor did God disapprove, but as He had not commanded it, feasting on a new moon was a social custom.
Perhaps feasting on the new moons began with families customarily making an annual sacrifice on one of them, as David mentions his family doing in Bethlehem (verse 6). Again, God nowhere commands Israel to do this. Commentators feel this feast was probably a thank offering on which the family feasted after God's portion was burned on an altar. They chose the new moons for these affairs, since they were not encumbered by the restrictions of God's law as the weekly and annual Sabbaths were.
John W. Ritenbaugh
The New Moons