Why is the melting point of magnesium nitride less than that of beryllium nitride?
Melting point in a compound with a lattice structure correlates more closely with lattice energy than with ionic character, and lattice energy tends to be greater when you use smaller atoms.  Among alkaline earth nitrides it is not just beryllium versus magnesium that shows this effect; it keeps going.  Melting point data below are from the Wikipedia articles as of April 30, 2021:
$\ce{Be3N2} = 2200°C$
$\ce{Mg3N2} = 1500°C$
$\ce{Ca3N2} = 1195°C$
$\ce{Sr3N2} = 1200°C$
The alkaline earth oxides show a similar trend, for the same reason.  Here the lattice energy of beryllium oxide is slightly depressed because each atom has a coordination number of only four whereas magnesia and its heavier congeners have coordination number six; thus the peak melting point is at magnesia:
$\ce{BeO} = 2507°C$ -- four-coordinate
$\ce{MgO} = 2852°C$ -- six-coordinate, same for the following oxides
$\ce{CaO} = 2613°C$
$\ce{SrO} = 2531°C$
$\ce{BaO} = 1923°C$