I'd say it makes even more unsafe for variety of reasons.
First of all, let's assume you live in a country where mains sockets and plugs are polarized and always wired correctly and there is never any wiring errors.
With only a single capacitor on Live and Neutral being directly connected, and each part being undamaged so no fauls in the components, the diode bridge negative terminal will always be within 1V of the 0V Neutral input voltage. Relatively safe and touching the output should not be deadly, but still, never touch it, and also such a device must not have any external connections because they are not isolated.
Of course if something is wired wrong and Live goes to diode bridge directly, the output is live and hazardous, as the 5V differential output rides on top of full 120VAC mains.
If you now put a capacitor on both Live and Neutral wires, assuming the capacitors are perfectly balanced and identical, with 120 VAC input, the output is still 5V differetial but riding on half mains AC with 60VAC common mode voltage compared to 0V Neutral.
May not be a deadly voltage either and again if every component is working perfectly, it should be fine, 60 VAC is approximately the limit of safety low voltage depending on your jurisdiction, but still, unisolated, and it should not be touched.
The second resistor being irrelevant to the subject and can be omitted, one resistor is enough for limiting inrush current but it could be split into two for symmetry.
But two capacitors in series needs to be double in capacitance to equal the capacitance of a single capacitor. If for some reason the Neutral side capacitor blows open, the Live side capacitor gives double the current than if it were a single capacitor design. Even the 1uF capacitor alone has impedance that passes 45mA at 60Hz, so it is also deadly alone, if for some reason the neutral is switched.
If either capacitor of the two short-circuits, it equals a single cap system that now provides double the current, which stresses the zener and it may overheat, damage, stop working and allow the capacitor that normally sees 5V to charge to much higher voltage, to about 180VDC.
Adding the capacitor makes it no more safe, it seems to make it only less safe.
It also does not depend on having polarized plugs or unpolarized plugs, as for safety reasons, these kind of capacitive dropper supplies must not have connections to outside world or otherwise exposed for users, these must be contained in a box with no user access to touch the circuitry.
It sounds safer that any fault will either open the circuit or cause large enough short so that the fusible resistor acts as a fuse, or a separate fuse blows, or in the event of neither, the circuit breaker blows, instead of just some amount of extra current that may ignite a fire.