Who will receive more votes (nationwide)?

[Pouring Rain and Blairing Music]

The media is bound to cover McMullin's poll numbers in Utah and give him enough of a boost to easily surpass Stein.

This is my thought as well. I crunched some 2012 numbers. That's an assumption that my not prove to be true, but it's the best we have.

Utah 40%  1017             407
Idaho 15%   652               98
Colorado 2%   2569          51
New Mexico 1.5%  784     12  
Minnesota 2% 2936          59
Iowa 1% 1582                  16
Arkansas 0.5%  1069          5
Louisiana 0.5% 1994        10
Kentucky 0.5% 1797           9
S. Carolina 0.5% 1964      10
Virginia 2% 3854              77

                                     754(thousand)

I'd say that McMullin can get at least 750,000 votes on the ballots that he's on. That's using 2012 numbers, so it could be a bit higher.

Honestly, I could be way overestimating McMullin. However, he has had a number of articles and is getting some recognition. I haven't heard much from Stein lately and third parties have a history of declining numbers leading up to an election. McMullin seems to be an exception to that, with his numbers increasing as Trump's fortunes flounder in Utah. Honestly, I have no idea, but I'm sticking to it. Admittedly it would be unprecedented for McMullin to get that many write ins, but you never know, especially this year.

I am curious, what is the comparison with Thurmond?

[Pouring Rain and Blairing Music]

I am curious, what is the comparison with Thurmond?

In 1948, Thurmond won three states with an overwhelming majority, plus he broke 10% in several other states.
All those states are way bigger than Utah and Idaho, and in addition, McMullin won't reach those high percentages anywhere near.
All in all, Thurmond received 2.41%, only slightly more than the fourth contender in that four-way race:
Progressive Henry Wallace got 2.37%; his best state was New York (only 8.25%), followed by California (4.73%) and North Dakota (3.8%). In some further states he surpassed 3%, but in most he trailed way behind.
Nonetheless, Wallace was almost able to draw level with Thurmond.

McMullin, this year, will win big in Utah and do well in Idaho. However he has gained ballot access in only 11 states. Jill Stein is on the ballot in almost every state. She will win about 2 or 3 per cent in huge states like California and New York. And those are popular vote numbers McMullin cannot catch up with.

Conclusion: Constant dripping wears the stone.

I will say that one of the problems with the Thurmond comparison is how few votes were cast in the southern states compared to northern states of approximately equal population. That may have dampened Thurmond's vote numbers (now, granted a lot of the non-voters were blacks, who obviously wouldn't like Thurmond). I do get the point that you're making though; overall, it's not too bad of a comparison. Rather convenient, really. I'm just not sure that Stein will get that many votes.