What is the advantage of putting capacitors in parallel with glass fuse tube
The capacitor is placed for protecting fuse in switch on/off system.
Most loads are inductive such as motors and light bulbs, and in switching on or off, they will make a huge voltage from inductor equation, in switching on, this voltage will cause a huge current in a very little time, this can break your fuse without a SC, etc
By using this capacitor (typically ceramic) you can filter this current and protect your fuse from damaging from this current.