I myself made a mains indicator with an LED by using a regular diode across the LED in the opposite direction and a power resistor to limit the current. I don't see how that is more dangerous than a neon lamp which is made from glass?
Doesn't matter, All About Circuit's doesn't have a flat policy about Neon lamps from mains. They only care about LEDs from mains power. Some genius over there thinks current is somehow special and more lethal when LEDs are present vs when mains is a neon, incandescent, pump, electric fence, TV, etc
I myself made a mains indicator with an LED by using a regular diode across the LED in the opposite direction and a power resistor to limit the current.
Just make sure the resistor has a sufficient power rating.
For example, the resistor power dissipated for a 120V supply with a 10mA LED current is ~1.2W.
To avoid that loss, the current for a line operated LED is often limited by an AC capacitor of the appropriate capacitance and voltage rating, in series with a small resistor to limit the surge current during startup.
For example, for 120Vac, 60Hz, a 0.22uF capacitor will limit the AC current to 10mA with no dissipation loss.
A 1k ohm resistor in series will limit the startup transient current to a safe value (if the LED is turned on at the peak of the AC voltage).