Astrology would be a self-fulfilling prophecy if enough people took it seriously.
For example if everyone agreed on that Gemini means good at science and Leo is good at art, the whole education system would be designed around this belief and it would hugely impact how children think of their own potential.
There is a good example of this in Ancient Rome. By around the time of Augustus Romans were fervent believers in astrology. One of the most notable cases of astrology becoming a self-fulfilling prophecy has to do with the death of the emperor Domitian.
An astrologer named Asclation had earlier predicted that Domitian would die on September 18, 96 AD, and Domitian's enemies used this as a sort of nucleation point to organize his assassination. So although the date was made up, it had the effect of focusing the efforts of the assassins on a particular date, and they were successful in assassinating him on September 18.
The full story that survives probably has some embellishments, but is entertaining. As the day approached Domitian became increasingly nervous. On September 17, he called Asclation before him and asked him if he stood by his prediction. Asclation said he did. Domitian then asked Asclation how Ascaltion himself was to die. Asclation responded that the stars said that he would die by being torn apart by dogs. Domitian then had an idea, and condemned him to death by burning.
Asclation was immediately led to a public square, tied to a stake, and a bonfire was built underneath him. Not long after being lit, however, it suddenly began raining and the downpour quenched the flames. In the wet mess, Asclation's stake tipped over and a pack of dogs found him and devoured him.
This development naturally did not put Domitian's mind at ease. The next day he became a nervous wreck. Around noon, he asked an attendant what time it was. The attendant, who was part of the conspiracy, lied and said that it was an hour later. Seeing that the danger had passed, Domitian relaxed and decided to take a bath. As he was about to go out, an official rushed in and asked for his signature on some documents. The official appeared to have an injury to his arm, but this official was also in on the conspiracy, and his sling concealed a dagger. When he got close to the emperor he stabbed him to death.
Chinese "sign years" are a good example where it seems not to shake out. There's a 12-year cycle between repeating signs, but it doesn't seem that every 12 years you get whole cohorts of specifically intelligent/kind/diligent/cunning/lazy/science-loving/humanities-oriented/whatever children in a given school year, which will nearly universally be composed of only two star signs (Chinese New Year falling about halfway into the school year). It's even more obvious on the 60-year "element-animal" cycle that the world doesn't go 3 generations between people having "fire dragon" or "earth horse" characteristics.
It'd be hard to hide such statistical effects on an yearly interval, whereas the Western zodiac hides its predictive failures by not having signs that are commonly stratified into different groups.
For example if everyone agreed on that Gemini means good at science and Leo is good at art, the whole education system would be designed around this belief and it would hugely impact how children think of their own potential.