with blues = photography
without = photo illustration
I could go either direction, but to belie the presence of indigo illuminators is deceptive unless you are after an illustration of the event, and not a mere photographic recording. 
That’s a worthy point to consider. However, our eyes and brains get adjusted to the lighting in real life and perhaps wouldn’t perceive it as drastically blue as the camera objectively renders it, so it makes sense to at least even it out a bit.
That’s the reason we usually do white balance, too: The yellow or blue cast you get on a photo with incorrect white balance is really an accurate depiction of reality. It’s just that we don’t perceive it that way in real life, so it strikes us as very odd when we see it in a picture. So we change it to a more neutral representation which looks more natural to us.
In the end it must be the decision of someone who saw the event in the first place what they perceived and what would be a worthy depiction of it.
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The way I understand the problem, it is caused by blue LEDs. The camera is much more sensible to UV light than the human eye, and consequently it renders the blue lights coming form LEDs the wrong way. Maybe some day camera manufacturers will take action and tweak their sensors in a way that keeps this in consideration. In this forum too I’ve read many posts about the blue LEDs’ problem. @s7habo published one of his remarkably excellent “Editing moments” video tutorials to this matter Darktable Episode 66: Difficult lighting conditions - YouTube
And, if I remember correctly, Aurélien Pierre also touched on the subject in one of his videos (that I can’t find right now).
Having said that, you want that blue light back (together with its companion over-saturated yellow shadows)? That would be an easy editing, but supposedly it won’t be faithful to the original scene.
Ideally you should be able to compromise and render the original lights without the blue-bug of camera sensors, but, as you said, this would imply you should have been there when the shot was taken.
@Thomas_Do Your nice cyan edit made think about Topor’s Planete Sauvage https://www.google.com/search?q=Topor+Planete+Sauvage+Japanese+poster&tbm=isch&ictx=1&tbs=rimg:CQlw2iAQnt5HIggJcNogEJ7eRyoSCQlw2iAQnt5HEVoO8-zGHqzx
You scoundrel.
What I experienced at the event was not purple-faced people, and not purple shirt / dress. To my eyes, the scene looked almost neutral. I noticed the blue LEDs (which were facing the stage) only when I went to the light stands and checked.
So, I do not mean to completely neutralise the blue; but the camera sensor + the camera’s processing is very far from my eye’s sensor + my brain’s processing. I never saw these featureless purple faces, or that muddy-looking shirt:
The red is actually important. The lady is Vera Karinthy, great-granddaughter of Hungarian writer Frigyes Karinthy. Frigyes died in 1938, two years after brain surgery due to a brain tumour. At the beginning of the 1930s, he became obsessed with the colour red, which may have been one of the first signs of the cancer. That is why Vera wore a red dress and the man, Tibor Bornai, wore a red shirt, and why the band of his wristwatch was also red, just like that of Frigyes. He even wore red shoelaces, which was never recorded about the writer. 
We all know that blue LEDs are problematic, that people are very often dissatisfied with their cameras’ / softwares’ rendering. Here, the problem is probably accentuated by all the red on the stage, and how the atmosphere of the event (laid-back discussion and sharing of memories and family stories) conflicts with the lights (which were not elements of the ‘show’ like how they may have been elements of a concert).
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I like to know the background historic information. And the story about colors is very consistent with this Play Raw, in many ways. I’ll look for Frigyes Karinthy, thank you.
He was the one to translate Winnie the Pooh to Hungarian, and was also a great writer and parodist in his own right.
I happen to have attended Karinthy Frigyes Gimnázium
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One more from me, taking some ideas from your contributions. I think it was @anon42681393 who used color calibration with grey mixing, blended for the blue channel.
2023-03-10_19-12-33_P1080015_09.RW2.xmp (21.1 KB)
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Best I could do. Chose blue and set to grain extract with original layer on base and copy of original layer above the grain extract layer set to Lhc Lightness. Did some selective blends to get some blue back on certain things as well.
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Turns out that no-one wants to see the blue led light shining through as seen in my previous reply. This is a nice image to play with so I spend a bit more time using a somewhat different approach.
Blues be gone!
RawTherapee 5.9 dev
Not sure if I should have pushed the chromaticity/saturation up a notch or two, decided against it in the end.
PS: The sidecar should work on normal, stable RT 5.9. No dev and/or mergers needed 
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As I just ended work I was ready to give it a try but at the same time I thought if you had the time to try you’d nail it, and sure you did !
As some other did.
Congrats 
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2023-03-10_19-12-33_P1080015_02.RW2.xmp (18.1 KB)
One simple version and a second with a hue shift applied…
Ironically landed on it messing with the base curve…
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Very well done, Todd!
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ART
Not quite satisfied with first trial. went more neutral. Not sure this one is better! These blue leds are a nightmare!
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2023-03-10_19-12-33_P1080015.RW2.xmp (32.7 KB)
I though it would be fun … pushed to the extremes, colour correction is not so stable… or I do not know how to manage it properly. Ended up fixing patches with look-up table
Multiple directions, one can take here. Appreciate this very interesting image with difficult lighting conditions. I tried to concentrate on the skin tones and then give a plausible colors to the other parts of the image.
2023-03-10_19-12-33_P1080015_01.RW2.xmp (35.5 KB)
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Wow, seems like the Tone Equalizer did some very nice clean-up!