Yes, there are false believers and plenty of them. Same as in Bible times except probably a lot more because there are a lot more people in the world. What is a False Believer? Let's do a little studying and find out, OK?
Isaiah 29:13 "Therefore the Lord said: In as much as these people draw near with their mouths and honor Me with their lips, but have removed their hearts far from Me, and their fear towards me is taught by the commandment of men." Matthew 15:8 says the same. We can talk like we are a saint and honor God with our mouths and our hearts may be far from Him and we may be living a lie.
Luke 6:46 "But why do you call Me 'Lord, Lord', and do not the things which I say." Our mouth is getting in the way again. This sounds like a hypocrite, doesn't it?
John 14:6 "Jesus said to him, 'I am the way, the truth and the life. No one comes to the Father except through Me." This is the only way that we can come to the Father, is through Jesus our intercessor. It is the only way we can be secure in our faith and beliefs, if Jesus is the way, the truth and the life, then this is the way for us to follow.
Titus 1:16 "They profess that they know God, but in works they deny Him, being abominable, and disobedient, and unto every work reprobate." By their fruits you will know them, we cannot judge motives but can see what kind of fruits are visible.
James 1:26 "If anyone among you thinks he is religious, and does not bridle his tongue but deceives his own heart, this one's religion is useless."
1 John 2:4 "He who says, 'I know Him', and does not keep His commandments, is a liar, and the truth is not in him."
1 John 2:9 "He who says he is in the light and hates his brother, is in darkness until now."
1 John 3:6 "Whoever abides in Him does not sin, (willfully)Whoever sins has neither seen Him or known Him."
Do these verses explain what a False Believer is. I think they are pretty plain and the only way we can be secure against error is to study to show ourselves approved by studying His word which is what we are doing just now. Our strength to do His will comes only from Him who is the way, the truth and the life. Press on friends, Christ is our hope, our only hope in this wicked world. Grandma