The dragnet that is cast into the sea was probably similar to this seine net these fishermen are using in the photo. It has floaters on the top and weights at the bottom so that it spreads itself from the surface to the bottom of the sea and is dragged between two boats to capture a school of fish. Once filled, the fishermen draw it up on the beach and sit down to separate the desirable fish from the undesirable.
Naturally, the net is indiscriminate in the kinds of fish it captures, just as the gospel goes out freely into the world and invites into the kingdom all who would come. So the kingdom is a mixture of the righteous and the unrighteous, and according to this parable there is something inevitable about that. This illustration parallels a previous parable Jesus told in this chapter about the wheat and the tares, except on this point. With the wheat and the tares, it was an enemy who planted the tares among the wheat, and the harvesters waited until both plants grew to maturity before they could gather up the invading tares and burn them. Here, the good fish and bad fish are naturally mixed together, and the net sweeps them up as it finds them. There is no sinister plot to plant unwanted fish into the net. The implication is that the gospel is designed to gather a mixed catch; it is to be expected.
So from one perspective the devil is infiltrating the kingdom with his own false sons (wheat and tares), but from another perspective God knowingly casts his nets wide enough to receive, temporarily, both true and false sons into the church community (good and bad fish). Whatever Satan's plans may be, he cannot escape God's sovereign control of the situation and its outcome. God is not surprised to find the devil's children in his nets and in many ways he expects it. He has offered the gospel freely and generously. What matters is that at the end of the age the angels will be sent out to separate the righteous and destroy the wicked in the furnace of fire.
Who are the good fish that are gathered up? Looking back at the parables in this chapter, they are the good soil upon which seed was thrown, which sprouted up and yielded fruit up to a hundredfold. They are the wheat that grew to maturity in the field, distinguishing themselves from the false tares. They are the ones who gave up all their worldly goods to possess an infinitely more precious heavenly treasure. By their lives they have shown themselves worthy of the kingdom. This is not about works salvation, but about having true sight to see what really matters, and possessing true faith which produces a life reflecting the values of the heavenly place that you seek.