The issue seems to be that Skylake uses a thinner substrate, which can make the chip flex under pressure due to lower mechanical stability. High-pressure CPU cooler mounting systems can reportedly exert so much force on the CPU that it can damage both the motherboard and the CPU pins.
Heatsink maker Scythe acknowledged the issue and offers customers a new set of screws free of charge:
Japanese cooling expert Scythe announces a change of the mounting system for Skylake / Socket 1151 on several coolers of its portfolio. All coolers are compatible with Skylake sockets in general, but bear the possibility of damage to CPU and motherboard in some cases where the PC is exposed to strong shocks (e.g. during shipping or relocation). This problem particularly involves only coolers which will mounted with the H.P.M.S. mounting system*. To prevent this, the mounting pressure has been reduced by an adjustment of the screw set. Of course, Scythe is going to ship a the new set of screws to every customer completely free of charge! To apply for the free screw set, please send your request via e-mail to support@scythe.com or use the contact form on our website.Here's a brief overview of some comments from other HSF and waterblock makers. Most say there's no problem with recent coolers but advise caution if you plan on transporting your PC.
*Following coolers use this mounting system:
Ashura, Mugen 4, Mugen 4 PCGH-Edition, Fuma, Ninja 4, Grand Kama Cross 3, Mugen Max & Kotetsu.
Via: eTeknixNoctua: No issues with SecuFirm2 mounting systems cause no issues with Skylake but remove coolers with a weight in excess of 700g during transport.
Alpenföhn: No issues, but remove heavy coolers during transport
EK Water Blocks: No problems with EK-Supremacy coolers with PreciseMount but older waterblocks like the Supreme LTX may cause issues.
Arctic Cooling: No problems, but be careful with transport.
ThermalTake: No problems, systems with heavy coolers should be transported flat.
Thermalright No issues, but remove heavy coolers during transport.