Since no sane person would really open that door, how does this consideration prompt allegorical readings of the story?

Connie going through the door is symbolic on a number of levels. Doors, windows, and thresholds are common metaphorical symbols in coming-of-age stories such as this one. On one level, these structures represent the leaving of one particular phase of life and crossing over into another. Sometimes that phase can be from death to rebirth (usually symbolic), or from innocence to knowledge. The movement from innocence to knowledge is also seen in the loss of virginity, and given Connie's earlier sexual experimentation, it can be said that her sexual curiosity outweighs her fear and repulsion in her decision to open and go through the door. But since the story does hint at being symbolic and allegorical, then Arnold Friend may not be a literal lover who appears but a representation of that first sexual experience that Connie is drawn to, yet apprehensive of.
Arnold Friend represents secrets and realities of adult life that Connie finds frightening yet alluring. The story is dedicated to Bob Dylan, and we can surmise that the figure of Arnold Friend is something of a composite of all the fantasies and wishful thinking that Connie superimposes on young men in her life based upon the popular music she listens to, and Dylan's musings about love and rebellion were surely in the rotation that she listened to on the radio. Opening the door represents opening the conscious mind to experiences and ideas, and the popular music of the period was known to be aligned with the modes of consciousness exploration that became popular in the late 1960s when the story was published. Those modes also included meditation, hallucinogenic drugs, and the occult arts (such as astrology, tarot, etc.), as well as practices found in Eastern religions such as Buddhism. Consciousness exploration was a subject of the music by many popular bands of the day like the Beatles, Jefferson Airplane, and the Moody Blues (who made one album entitled "On the Threshold of a Dream"), and these ideas were picked up by the youth culture of the time via that music.