Is the value of XTAL load capacitors for ATmega328p @ 16MHz critical?
Your title asks about the value of the capacitors, and I think that has been adequately covered- you should match the nominal value to the specified load capacitance of the crystal (when in series with each other, and subtracting some allowance for input and stray capacitance). 

The Q of a typical crystal resonator circuit is very high (maybe 100,000), and a small change in load capacitance won't affect the oscillation frequency by much. The equivalent "motional" capacitance of the resonator is quite high, so the pull effect of the load is small (typically measured in ppm/pF). If you are not using the crystal for a time keeping clock, it probably won't make much difference for you- it will vary with the crystal and load capacitance, but, say 5pF might make 30ppm or 100ppm difference in the oscillator frequency. 

Since the capacitor might be 22pF, 5pF is a lot of change, so the tolerance and temperature coefficient is not very important. It's also cheap and easy to find almost perfect capacitors in the capacitance range used for load capacitors- ceramic NP0 types with tolerances of 5% are the cheapest and most available, and they're always rated for at least the voltage required (Vdd + 1.2V is certainly enough). Take the 27pF value- a Samsung CL10C270JB8NCNC is 5% tolerance, 50V, maximum drift of +/-30ppm/°C** and insulation resistance in the 10G range. All for $7.54 for a reel of 4,000 pieces, Digikey price. The difference between microwave and ordinary NP0 caps would not be noticed at 16MHz (except, of course, for the much higher price of the former). There are all kinds of complications (voltage coefficient, high temperature coefficient, microphonics, aging) associated with high value ceramic capacitors that don't apply much, if at all, to NP0 parts. 

TL;DR Bottom line- if you use the most common NP0 ceramic capacitors in your favorite size, your circuit performance will not be limited by the capacitors in virtually all cases. 

** Note that a 30ppm/K change of the load capacitor would likely contribute less than 0.1ppm/K change to the oscillation frequency (the temperature changes will be dominated by the crystal itself).