Grignard reagents can be viewed as extremely strong bases (sometimes analogous to a deprotonated alkane (Bruice), meaning a pKa of ~50) and can therefore deprotonate compounds that aren't normally considered "acidic".
For example, any carbonyl solvent is already a no-go as these usually contain acidic alpha-protons and are also electrophilic. Acetonitrile, di- and tri- chloromethane and similar compounds are probably acidic enough to be deprotonated by a Grignard reagent, as well as primary and secondary amines.
Aliphatic ethers are great because they are somewhat polar, which allows for them to dissolve a wide array of organic compounds (namely esters, aldehydes and ketones in the contenxt of Grignard reactions) while being entirely aprotic. In theory you could also use hydrocarbon solvents (pentane, hexane, heptane, etc.), but the solubility of your reagents may be very limited.
Can't vouch 100% for everything said here, I'm just using my chemical intuition. After all, whatever happens in the reaction flask decides what's true in this field.