Why does He allow them to deceive us with their false Doctrines? What is God's purpose in allowing False Prophets to exist?
Because God is a loving God,that is not whipping their butts,but nobody will get away with anything.
It appears for the most part that God allows things to run their natural course,and will intercede to put things on a good course,but since we have a choice between good,and evil,thanks to Adam,and Eve,and I do not mean that in a good way,at least the evil part,then for the most part things happen,because they happen.
If people say why does God allow false prophets,and hypocrites,that deceive people,then why does God allow people to put out pornography,and alcohol,and cigarettes,and drugs,and worldliness,and all other things that are bad,that tempt Christians,and cause some to err.
We are under grace,and the Bible says that God rains on the just,and the unjust,for all get a reward,some choose it in this world,some choose it to be in the spiritual world,which Jesus said the Pharisees have their reward,and a hypocrite has their reward,like the Pharisee.
It appears God allows it to happen,because for the most part God allows things to run its natural course,and will intercede for good,but will not violate our choice,and we are under grace,and it appears for the most part,that God does not go against people like He did in the Old Testament,when back then,He would put down people that caused the Hebrews to err from the truth,but He did allow Jezebel to deceive for a while,but then she was put down.
God is love,but if they are false then they do not have God's protection,which something bad might happen to them,not coming from God,but God allowing it,for they do not have God's protection.
If you are led of the Holy Spirit,you cannot be deceived,and we all have access to a Bible,so if somebody does not take the time to read it,and know the truth,then they might be deceived,but some ignore the truth,wanting to believe what they want to believe,that read the Bible.
Falseness has to happen,and will happen because there is a lot of people that do bad,more than do good,for the saints cannot be united with Christ,until there is a falling away first,which is when there is a unified religious system,and all religions are valid,and they will only want to hear the word of God,according to their own lusts,which goes beyond material things,and money,which happens because God is allowing the world 7 years to have their way,and cause all people that do not love Him,to follow the beast kingdom.
God's word is still available at that time,for His truth will always shine forth,but people will have an occult interpretation of it,believing they can harness the power of nature.
Falseness will occur,because God is going to allow the world 7 years to have their way.
2Ti 2:19 Nevertheless the foundation of God standeth sure, having this seal, The Lord knoweth them that are his. And, Let every one that nameth the name of Christ depart from iniquity.
2Ti 2:20 But in a great house there are not only vessels of gold and of silver, but also of wood and of earth; and some to honour, and some to dishonour.
2Ti 2:21 If a man therefore purge himself from these, he shall be a vessel unto honour, sanctified, and meet for the master's use, and prepared unto every good work.
God said there will be some hypocrites,and there is a whole lot more of them at the end time,but it is still a great house,for hypocrites do not belong to the Church,but God is not going to strike them down if they go to Church.