In 1937, when HMS Hood was part of the Neutrality Patrol off the coast of Spain, red, white and blue stripes were painted on the B turret. All of the ships that participated in the Neutrality Patrol had these stripes, which allowed easy identification and prevented them from being attacked by airplanes.
There is a color movie from June 1939 showing HMS Hood leaving Portsmouth, but there are no stripes on B turret and the turret is painted the same shade as the hull. The turret roof is not red either. Those were the only two color images of HMS Hood that have been posted on /r/Warshipporn . The Hood is one of the most frequently posted ship on that sub-reddit. There was a long discussion about the 1937 image. People wanted to know why the Royal Navy painted what looked like a Dutch flag on the B turret of their largest warship in 1937.

Hood was, at the time of her sinking at the Battle of the Denmark Strait, painted in a uniform colour scheme, unlike what the game portrays. She had received this painting on the 12th May 1941, about two weeks before the battle. She was painted in what was known as Pattern 507B, which was standard camouflage for ships of the Home Fleet. This pattern called for the ship to be painted a colour called Home Fleet or Admiralty Dark Grey, which, by WWII was a dark grey with a slight blue tinge - reasonably close to what the game displays (it is tricky to tell, thanks to variations in paint colour, and the poor quality of colour film available at the time whether the game's exactly correct). While Hood was on foreign stations, as she was between 1936 and 1939, she was painted in Pattern 507C, a lighter uniform grey, but retaining the blue tinge. Her turret sides were almost always painted the same colour as the sides of the ship, contrary to what the game shows. The only exception came in early 1941, where she was painted in a multicolour scheme. In this, her hull was painted 507B dark grey, but her A turret (foremost) was painted a lighter grey, possibly 507C, while the B turret (just astern of A) was painted a darker grey or the new, 507A, which was a matte variant of 507B. Her turret roofs wore several colours over her lifespan - sometimes the same colour as the sides, sometimes grey or black to match the painted metal decks. During the Spanish Civil War, she wore several markings to show her neutrality, painted on the roofs of A and B turrets. A turret had a marking like an aircraft roundel, as to help aircraft identify her. B turret had red, white and blue stripes painted across it, for identifying her to other ships. She seems to have retained the marking on A turret during the war, though I can't confirm it was present at the time of her sinking.

Unfortunately the log book of HMS Hood was lost when the ship went down, which means we cannot be 100% certain of when the ship was last painted. The last confirmed painting took place on 12th May (so a little short of two weeks before being sunk). It may well have been painted again after this time, but we just cannot know.

What we do have are black & white photos taken of the Hood while en route to its final battle, as well as underwater photographs taken of the hull in more recent times. These appear to show that Hood appeared more or less similar to the color scheme applied on 12th May. This would be a uniform coating of Admiralty Dark Grey (Admiralty Pattern 507B) on all vertical surfaces and main turrets, plus dark/dull mahogany colored wooden decking. It may have had a roundel painted on top of "A" turret, but that is uncertain.

Thus the overall uniform blue/gray color scheme in your picture appears correct, but the white/red combo seen on the turrets looks to be faulty.

That said, painting all/parts of the tops of turrets or main decking in different/bright colors was not unheard of during WWII on either side. This would have aided recognition from the air, and could be applied if operating with local air superiority, thus lessening the chance of mis-identification by friendly air reconnaissance or being attacked by friendly aircraft (such as actually happened to HMS Sheffield during operations to hunt down the Bismarck).

Unusually my main source for this is web-based, rather than printed and published. This is somewhat unfortunate, but the HMS Hood association appears to have done decent research.