As with amps of any type, there's a lot of variation among Class D amps. But objectively speaking, they seem tailor-made for difficult loads, given their high power and high damping factor. But much will depend on the power supply and modules used. The field has been moving fast, with consensus opinion being that current Class D modules sound better than those from only a few years ago. Contemporary amps built around Hypex and PuriFi modules seem to be generally admired at their price points.
I have long-term personal experience with Devialet's Expert Pro line of Class D integrated amplifiers, and they are fantastic on difficult loads. Talk to David Hyman (who is hosting an SFAF event in Sauselito in a few weeks), who bought my Devialet Expert 1000 Pro amps to drive his very difficult PMC Fenestria speakers, which defeated several high-end Class AB behemoths.
But as with all things in this hobby, there's not generalizable answer for all Class D amps or all speakers. Try some out -- I'd start with something like the NAD C298 or M23 (built around PuriFi modules) or a Devialet Expert Pro (used prices are very good!).