Lightroom/Camera Raw: Camera Standard profile for A7R III is terribly off

Some examples would help diagnose the issue.  Can you post screenshots? 

Do the exported versions of your pictures when using this profile still exhibit the yellow cast?

You can fix this! .dcp profiles are white balance agnostic and users must still apply WB.

@Rikk, will do when I have a sec

@Andrew I know I can still fix it changing the WB but if Adobe got the profile right in first instance I would save time...Canon ones are very good.  What is the origin of the yellow cast, is it color rendition or the profile is also applying it's own white balance on top of color rendition and tone? With the Canon profiles I never experiences any color cast/WB shift.

There is no 'right' here! You have a warm cast; fix it. The profiles don't handle this by design. Or roll your own profile for your specific sensor:
Everything you thought you wanted to know about DNG camera profiles:

All about In this 30 minute video, we’ll look into the creation and use of DNG camera profiles in three raw converters. The video covers:

What are DNG camera profiles, how do they differ from ICC camera profiles.

Misconceptions about DNG camera profiles.

Just when, and why do you need to build custom DNG camera profiles?

How to build custom DNG camera profiles using the X-rite Passport software.

The role of various illuminants on camera sensors and DNG camera profiles.

Dual Illuminant DNG camera profiles.

Examples of usage of DNG camera profiles in Lightroom, ACR, and Iridient Developer.

Low Rez (YouTube):

http://youtu.be/_fikTm8XIt4

High Rez (download):

http://www.digitaldog.net/files/DNG%20Camera%20profile%20video.mov

I mean the other profiles (Adobe Standard, Sony Camera Neutral, Vivid etc) do not have the same cast, I assume it was a mistake on Adobe side when creating the profile rather than a  problem of my hardware?

Don't make such assumptions. Do shoot say a color checker in daylight and provide  example here AFTER WB. 

would love to but I don't have a color checker. Will see what I can do but other people have noted the same yellow cast using that profile.

While you are here, can you take a look here? https://www.dpreview.com/forums/post/60635548
Thanks Andrew!

The DPR post is kind of meaningless. CCT values define a range (a large range) of possible colors and differing values can define the same color! 
http://digitaldog.net/files/22Thecolorofwhite.pdf

You are The expert on the subject and I only have limited knowledge of color science so i struggle to follow you. All in all shall I be happy with the hardware calibration and profiling I obtained vs my targets (D65 for whitepoint) or have to do it again?
Thanks
PS probably worth contuining the whitepoint discussion on dpr and leave this thread to the profile discussion

There is only one object that can produce D65 (an average of many measurements) and its 93 million miles from your display.

So the short answer is that I shall be happy with the result achieved by the calibration (despite the dispcal fail)? Would appreciate a straight, non technical answer, thanks

What calibration? You are working with generic .dcp profiles. For display, the values WILL vary.

About display calibration targets:
Why are my prints too dark?
A video update to a written piece on subject from 2013

In this 24 minute video, I'll cover:

Are your prints really too dark?
Display calibration and WYSIWYG
Proper print viewing conditions
Trouble shooting to get a match
Avoiding kludges that don't solve the problem

High resolution: http://digitaldog.net/files/Why_are_m...
Low resolution: https://youtu.be/iS6sjZmxjY4

@Rikk

Going back to the main topic. Here is an example. 
Left is camera Standard, right is camera Neutral (also Adobe Standard looks similar)

You can see there is a yellow cast in camera Standard (eg color of the wall). Also, I was shooting in RAW + Jpg with Standard profile and in the jpg file there is no yellow cast.

Comparing the DNG and JPG images on DropBox, to me it looks like all the Camera xxxx profiles have stronger yellows.  This is NOT the same as saying there is a yellow color cast because neutrals still seem neutral so no overall cast where whites are yellow, but the yellows are stronger.  Since the image does not have a full range of colors it is difficult to tell if it is only yellows or various other colors--do you have any market scenes with a range of vibrant colors?

Here are some comparisons the camera JPG and camera DNG with no corrections in LR, using side-by-side Reference View (Shift-R) mode:

First, here is using the Adobe Standard profile, which has slightly muted colors and in my opinion even weaker yellows than the camera JPG:


Here is the Camera Standard comparison where the yellow on the wall at the top right is more intense:


Here is the somewhat closer result after messing with the Camera Calibration Hue sliders for a bit to make the Camera Standard DNG closer to the JPG, though it's difficult to say how well these adjustments would work with other images with more colors:


One final comment is that checking the JPG metadata in EXIF Tool, while most settings are Standard, it appears that Dynamic Range Optimizer was set to Auto and if the camera actually did some auto-fixing before creating the JPG this could make things slightly different than whatever Adobe used when they did their calibrations and can make matching a RAW to a JPG a moving target from one photo to the next: