Is resistor/capacitor in parallel to the transformer primary (adequate) inrush protection?
No, that will not affect inrush current and in fact it's just a neon lamp + resistor to indicate power on. 

For inrush current limiting you can use an NTC thermistor or one like this in series with the primary. It's imperfect though- the resistance drops when it gets hot so if the user flips the switch back and forth with it hot, you can get the fuse blowing if it's not an appropriate slow-blow fuse type. 



Another approach is to put a power resistor in series with the primary and short it after a second or two with a relay contact. You must use a fusible resistor so if (when) the relay fails, the resistor will burn out without causing undue excitement, sirens, etc. 

Edit: BTW, it's also possible that the problem is not the inrush current (especially if this is not a toroidal transformer) but sparking when the power is removed or the switch bounces. In that case, an MOV across the input 230V at the transformer (after the switch) and/or a surge protector on the devices that are affected may help.