Is this passive headphone mixer design safe?
With 1K ohm resistors it is probably safe, but it will sound marginal to terrible.  I wouldn't do a passive mixer for anything with inductive or capacative loads (headphones, speakers, etc.).  

If your purpose is to hear something, anything, and not blow up your stuff then this will be fine.  If your purpose is to actually enjoy music then don't bother.

Headphones (and speakers) need a low-impedance amplifier driving them.  If you have a high impedance (or use something like a 1K resistor) then you are essentially causing the frequency response of the headphones to go from hopefully flat to something not even close.  

Think of it like this...  

Impedance is basically a frequency-dependent resistance.  Your headphones have an impedance that can change a lot depending on frequency.  However, they are also designed so that (hopefully) the frequency response is mostly flat for a given voltage input, despite the wacky impedance graph.

Now you put a 1K ohm resistor in series with the headphone.  That resistor, plus the impedance of the headphone, form a voltage divider.  But the dividing ratio changes over frequency because the impedance changes over frequency.  That causes what was a flat frequency response to become very much not flat.