The fuse is used to protect the capacitor, so its fusing current is far less than the maximum current that the capacitor can bear. Therefore, when the current in the line reaches the fuse opening, the capacitor can still bear it without damage.

Capacitors amplify harmonics. Because the capacitor pair is connected to a higher frequency current, the impedance is lower. Therefore, when there are harmonics in the power grid, the impedance of the capacitor to harmonics is much lower than the normal impedance at 50Hz, which will cause harmonic current amplification. This is the reason why harmonics easily lead to fuse blowing.