Does milk worsen the amount of mucus in the lungs for Cystic Fibrosis?

For those that are not aware, Cystic Fibrosis is a genetic disorder that affects cardic and digestive ability by damaging internal organs such as the liver and stomach (by removing the ability to process food with enzymes) and worsens lung capacity.

I have recently heard the claim that milk may worsen how much mucus the lungs produce. Specifically, those with cystic fibrosis may be affected. For example, both here and here claim that any milk-mucous connection is a myth, but in explaining the myth the second source claims:

Another potential explanation for the myth is that when milk breaks down, it releases a protein that is known to boost the activity of a gene involved in mucus production. But this particular mucus production happens in the bowel, not the respiratory tract, Balfour-Lynn said.

This mucus could affect the respiratory tract only if the bowel were weakened by infection, which would allow the mucus to travel elsewhere in the body, he said. This wouldn’t happen with a common cold, although it’s possible it could affect people with cystic fibrosis, which is sometimes accompanied by gut inflammation, Balfour-Lynn said.

I am finding this claim hard to believe and have done some research on google on how bad this may be, but have not found any article that says it does harm, but actually helps due to the calcium in the milk (reducing the risk of osteoparosis in further life) and has no affect on mucus amount. Can anyone help understand how true this claim is?

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I have found this article on a potential milk allergy for people with Cystic fibrosis and how it may lower zinc concentration in the pancreas, but I don’t think this is directly related to the claim made.