Does God accept wrongly done worship if the heart is right?

Answer:

Before Hezekiah became king, the worship of God had been stopped for decades. "For our fathers have been unfaithful and have done evil in the sight of the LORD our God, and have forsaken Him and turned their faces away from the dwelling place of the LORD, and have turned their backs. They have also shut the doors of the porch and put out the lamps, and have not burned incense or offered burnt offerings in the holy place to the God of Israel. Therefore the wrath of the LORD was against Judah and Jerusalem, and He has made them an object of terror, of horror, and of hissing, as you see with your own eyes. For behold, our fathers have fallen by the sword, and our sons and our daughters and our wives are in captivity for this" (II Chronicles 29:6-9).  When Hezekiah became king, he was determined to restore the true worship of the true God.

But where do you start? No one had been following the laws of purification and the temple had been used for idolatry. The priests and Levites began by clearing out the temple and cleansing it (II Chronicles 29:16-17). Offerings were once again made, but there were not enough consecrated priests to handle the load, so Levites stepped in to help until more priests could be consecrated (II Chronicles 29:34). This same shortage led the leaders to delay celebrating the Passover that year (II Chronicles 30:2-3). Such a delay was allowed in Numbers 9:10-11.

Many in Israel refused to come to Judah to celebrate the Passover, but still, some responded to the invitation (II Chronicles 30:10-12). Even then, the crowd that came was huge. More priests and Levites consecrated themselves (II Chronicles 30:15). Because many of the people who came had not consecrated themselves before coming, the Levites did the slaughtering of the lambs on their behalf (II Chronicles 30:17). Having not followed the law in so long, it is understandable that many didn't know the rules that were supposed to have been followed. Hezekiah understood this but asked God to show mercy and overlook this flaw this one time (II Chronicles 30:18-20).

God heard Hezekiah's prayer and healed the people; that is, He pardoned them of their sin (Isaiah 6:10). This does not imply that God would do the same the following year. This was an unusual circumstance for which God offered mercy because they were trying to return to following Him.

This shows God's mercy, but it is not an excuse to sin and assume that God will overlook the continual ignorance of His laws. "What shall we say then? Are we to continue in sin so that grace may increase? May it never be! How shall we who died to sin still live in it?" (Romans 6:1-2).