I just finished watching the Hello,Dolly! Blu-ray and thought it looked beautiful. I am a big Barbra Streisand fan and saw this movie many times at the Chinese Theater in Hollywood the year it was released. Personally, I see nothing in this Blu-ray that wasn't largely the way it looked in that theater in 70MM on its initial release. That includes skies, skin tones, costume/fabric colors, everything.
Now, I will say that there is very little blue in this movie to begin with. That has nothing to do with the sky issue, but with the general production design of the whole movie. Sure, there are thin blue patterns woven into Cornelius' suit, Vandergelder's suit in some scenes will have a bit of a bluish tint in the grey, and Minnie's night on the town outfit is a lovely light blue. But, IMO, if you want to know why there is so little blue in the general production design, one has only to look at Streisand's eyes in her close-ups. I suspect the production designers, producers, et al were very conscious of making sure their number one star was not upstaged by anything under their control. And if her blue eyes were going to pull the kind of audience focus the filmmakers and the audience demanded in those post-Funny Girl blockbuster hit days, nobody was going to surround her or anyone else with blue sets, blue curtains, blue costumes, etc.
IMO, the "don't upstage the Star" factor also pertains to the casting of the secondary leads. Not that this directive would come from Streisand herself, but she had at that time teams of management and agent representation that were all about developing this Mega-Super Star's full potential. And her fans expected nothing less from them. That would include making sure that whoever was cast in those secondary leads was not some stealth Movie-Star-In-The-Making whose personal charm and star quality would steal the show from her or Matthau, who was also a super star product of the day. Streisand had just come off a major hit in Funny Girl, where she was paired with a handsome matinee idol level leading man in Omar Sharif. A few years after Hello, Dolly! she would be paired to great box office success with another matinee idol level leading man, Robert Redford. Despite Barbra's unconventional good looks, audiences bought these pairings with gusto. Consequently, I think that accounts for the decision to go with the "goofy" Cornelius instead of the good looking Cornelius along with a lovely but rather un-charismatic secondary leading lady. Nobody behind the cameras was going to have some rival Prince Charming-Cinderella story going on while Barbra was wooing and winning a character written to be an old curmudgeon, risking that audiences might be drawn to and embrace the Prince Charming and the Cinderella over their stars' pairing, I'm sure nobody at the casting office or in the Producer's office was searching for the next Shirley MacLaine or the next Tony Perkins. Not this time.
As far as the whitish skies go in the scenes shot at the Fox Studios, what I saw on the Blu-ray is the same thing I saw in the 70MM screenings at the Chinese Theater Hollywood way back in 1969 (other than the occasional blue patch of sky here and there); a typical Los Angeles Basin overcast sky.
Fox Studios was then and still is located on West Pico Blvd, in Century City, not far from the beach and not on the San Fernando Valley side of the greater metropolitan L.A. area where a few other film studios are located. The San Fernando Valley side of L.A. is where you'll more likely get predictable blue skies much of the year. But Fox being on the beach-side of the "basin" means you'll get grey, overcast skies most of the year. See, the hot air on the San Fernando Valley side of the hills ("mountains", to L.A. residents) pulls cooler air over the Pacific Ocean into the L.A. Basin. When that cooler air slams on the "city" side of L.A. slams into the hotter air on the San Fernando Valley side (over the hill, it's really a desert area), you get haze. Most of the year really. What I saw of the sky in that movie is exactly what I had seen for lo' those many years I lived in the area, at one time or another on each side of those mountains; a hazy, overcast sky.
BTW, many filmmakers don't like "blue skies" in their movies. I can imagine the producers of Hello, Dolly! being somewhat relieved that they had few of them to contend with in the Fox Studio shots. Unless you're shooting in a location specifically known for their blue skies, getting a cloudless blue sky day after day on a movie shoot is a rarity. Consequently, having somewhat more innocuous and nondescript overcast skies make it much easier to match a certain look on turn-around shots.