What's the real inrush current in my AC/DC rectifier?
The inrush current is a very short (in time) event.
A fuse is a (comparatively) slow device, the wire in the fuse needs to heat up. It needs to collect a certain amount of energy over time to heat up and melt.
If the inrush current pulse integrated over time does not exceed a certain value, the fuse will not blow.
Did you ever notice that fast and slow fuses exist ? But even the fast fuse might be too slow in your case. Which is good, you only want it to blow of course when something is seriously wrong.

Additionally the 18.6A might be optimistic. I mean that in practice it will probably be lower. Did you take into account the DC resistance of the secondary side of the transformer ?