The mustard seed grows into a tree and that is a form of wild growth. Mustard is a vegetable and mustard bushes can grow quite high, but it will never develop into a tree. The original mustard seed that the Lord sowed in the world as a representation of the Kingdom of Heaven would degenerate.
birds
The birds of the sky, which we have seen are a representation of the evil one (Matt. 13:19) and of the evil spiritual powers in the air (Eph. 612), feel very much at home in this tree and nest in its branches.
The mustard tree has its roots deeply anchored in the earth. This is also the case with religion. People exert influence in politics and society. For example, we see that when something happens in the Roman Catholic Church, it is news. It gets attention, because the church exercises power and influence in the world. And of course that is not only the case with the Roman Catholic Church, but all of religious Christianity has that intention.
other examples with birds
We often find stories in Scripture in which birds play a negative role. For example, when Abraham wants to offer a sacrifice to God, the birds want to prevent this and Abraham has to chase them away (Gen. 15:11). They want, just like in the parable of the sower, to steal what belongs to the Lord.
the butler and the baker
When Joseph interprets the dreams of the butler and the baker, the butler ends well (Gen. 40:9-13). After three days, he is exalted and receives his position as butler from Pharaoh back.
In the baker’s dream, the baker has three baskets on his head with bakery goods in them. The birds then come to eat what is in the basket. Joseph gives a negative interpretation of this dream. After three days, the baker will be hanged and the birds will eat his flesh (Gen. 40:16-19).
Most birds in the Bible are unclean (Rev. 18:2), such as carrion eaters (Rev. 19:18) and they are associated with death. They symbolize Satan and his messengers, he is ‘the one who has the power of death’ (Heb.2:14)
the tree of Nebuchadnezzar
In Daniel 4 a dream of Nebuchadnezzar is described. He dreams about a great tree, whose height reached to the heavens and which could be seen to the end of all the earth. Its leaves were beautiful and its fruit was abundant, there was food for all. The beasts of the field found shade under it, and the birds of the air dwelt in its branches (Dan.4:10-12).
In Ezekiel 31 we see something similar. There a tree is also described, whose trunk was higher than all the trees of the field. Its branches were many and its twigs long. All the birds of the air nested in its branches. All the beasts of the field gave birth to their young under its branches. All the great nations dwelt in its shadow (Ez.31:5-6)
prestige in the world
The tree in Daniel 4 appears to be a representation of Nebuchadnezzar himself and his Kingdom: the kingdom of Babylon (Dan.4:20-22). Not the Kingdom of Christ, but the Kingdom of people. The tree is a representation of greatness in this world. Nebuchadnezzar’s tree was cut down (Dan.4:23) and Nebuchadnezzar was put in his place and so will all human work end.
If we relate this earthly greatness to the parable of the mustard seed, which becomes a mustard tree, we see that what began with faith and was sown in the world by the Son of Man, grows into a monstrous tree, which begins to look suspiciously like Babylon.
Babel has always been religious, we know from the stories in the book of Daniel. And the last world empire that will have Babylon as its capital will also be highly religious (Rev.17:5).
opposite interpretation
The only other interpretation I know of this parable is exactly the opposite of the meaning, but it does illustrate that this meaning is correct. It is said that the mustard seed is the church. The church started out small and when we read the letters in the New Testament, we get the impression that the believers mainly met in their homes in not too large groups.
But within a few centuries, church institutions emerged with power and influence in the world and ramifications in politics and society. That the church has become great in this world is explained by these interpreters as something good and so this parable is given a positive application.
While the Lord had said that His Kingdom was not of this world (John 18:36), the church became great and of importance in the world. The world rejects Christ, but accepts the church. That should give food for thought.