You can install Ubuntu with UEFI and secure boot enabled without any problems (personal experience). I believe that several other distros work as well, out of the box. All distros can do UEFI with minimal effort.
To be honest I consider things like BMC and the like and whatever goes on inside the BIOS and the like as far greater opaque problems than some of the more esoteric security "assurances" like measured boot.
To be honest I consider things like BMC and the like and whatever goes on inside the BIOS and the like as far greater opaque problems than some of the more esoteric security "assurances" like measured boot.