"'Their deeds do not permit them to return to their God. A spirit of prostitution is in their heart; they do not acknowledge the Lord.'" NIV translation
The people had gotten so far away from listening to God that they even refused to acknowledge Him. Without acknowledging Him, there is no ability to be saved. Many have used these verses to support their idea that we can lose our salvation but that is not what it is talking about. This is talking about the fact that we can wallow in sin for so long and not listen to the call of the Spirit that we stop even hearing the Spirit. At that point, it is not possible to answer the call to be saved because you cannot even hear it anymore.
"'Israel's arrogance testifies against them; the Israelites, even Ephraim, stumble in their sin; Judah also stumbles with them.'" NIV translation
The Israelites, led by the tribe of Ephraim, decided that they did not need to follow God but could do things in their own way. They even got Judah to go along with them into rebellion. When we put our ideas and thoughts above God's, that is the ultimate in arrogance.
"'When they go with their flocks and herds to seek the Lord, they will not find him; he has withdrawn himself from them." NIV translation
God is a jealous God and so He does not share His position with anyone or anything. This verse speaks to the fact that the people wanted it easy in going to worship wherever they wanted but, then, wanted to turn to God when they needed His provision. As we see here, that is not how God worked back then and it is not how He works today. We cannot put our faith in a closet and only pull out worship and prayer when we need to ask for something. First and foremost, God wants us to have a personal relationship with Him. Then, we can share our needs and concerns with Him as they happen.
"They are unfaithful to the Lord; they give birth to illegitimate children. Now their New Moon festivals will devour them and their fields." NIV translation
They did not worship God in the way that He told them and so they were considered unfaithful. Because they taught those ways to their children, the children did the same and so were not really children of God (they were illegitimate). Their religious activity was not going to save them from the judgment of God and the same is true for us today. It does not matter how many times you enter a "church" building as that is not what brings salvation.