It seems that the WB calibration is messed-up for the 1DX Mark II manufacturer color simulation profiles.
For example, a WB value of 5100 +17 becomes 4300 -13 when using any of the manufacturer color simulation profiles instead of Adobe Standard.
Are you determining the WB value by sampling a WB card or ColorChecker shot in the picture using the WB eyedropper?
The "As Shot" values changes when changing between Adobe Standard and the other Canon simulation profiles.
However, after sampling a white area or card using the WB eyedropper, the value is locked regardless of the profile used and will result in wrong WB when changing between those profiles. I suspect that the WB calibration of the profiles are wrong, just like the "WB Calibration" value one might expect to work with when creating DNG profiles using DNG Profile Editor.
I downloaded a 1DX Mark II sample file here: Digital Cameras, Canon 1DX II Digital Camera Test Image
The As shot WB is 5350 -21 Adobe Std and 4350 -50 Camera Std, but the WB look the same for both. Using the WB Eyedropper I get 5700 -19 Adobe Std and 4650 -47 with correct WB (R=G=B). Clearly the "Camera" profiles are incorrect as the WB settings should be the same as Adobe Standard. My Canon 300d, 600D, and 5D MKII all show the same WB settings for As Shot or when using the WB Eyedropper.
However, after sampling a white area or card using the WB eyedropper, the value is locked regardless of the profile used and will result in wrong WB when changing between those profiles.
I'm not sure what you mean by "value is locked." When using the WB Eyedropper it changes the Temp and Tint settings to new values. If you change the Camera Profile the WB settings shouldn't change. The issue is due to different WB settings in the "Camera" profiles vs the Adobe Standard profile.
I modified the 1DX Mark II Camera Standard profile using Adobe DNG Profile Editor (DPE) as below and the values are now near identical (±50 Temp, ±1 Tint) to the Adobe Standard WB values for 'As Shot' and WB Eyedropper settings. Since I don't own a Canon 1DX Mark II I suggest you report the problem here: https://feedback.photoshop.com/photoshop_family.
Click on 'New Post' and follow the instructions and select Conversation Type> Problem. Please include a link to this post in the report and add a reply here with a link to the new report. Thank you! If you need help let me know.
DPE: WB Calibration changed to Temp -11, Edit> Reset WB for Current Image, save new camera profile in 'User' folder.
This has been been fixed in LR 6.6 and CC 2015.6. If you previously adjusted the WB using any of the Camera Matching profiles it will be necessary to readjust those image files after updating to the latest version of LR. Image files using Adobe Standard (with or without adjustments) are unaffected.