Why did public opinion became a new factor in politics in the second half of the 18th century?

Because public opinion is very crucial in winning elections in a democratic government.

Explanation:

Prior to the 18th centuries, monarchy is still the more popular form of government. In this form of government, Public's opinion does not really matter since the seat to the leadership position was passed through inheritance alone (the kings' son was guaranteed to get the throne)

In the second half of the 18th century, more and more countries started to adopted a democratic form of government to replace monarchy. In democratic system, people choose their own leaders through election. Because of this, public opinion toward a certain candidate could massively improve their chance of winning the election.