You have presented a challenge there. My suggestion is this - it may not be the dairy as such but the iodine that it carries.
Although use of iodine as a teat disinfectant appears to have reduced (not at all sure of the figures) it certainly used to be a very significant contribution to our iodine intake. And dairy anyway does have a significant iodine content.
Have you ever noticed any impact from other relatively high iodine foods such as some sea-foods? Do you use iodised salt or products that contain iodised salt?
Excess iodine *can* cause an increase in thyroid hormone levels. And some people are much more susceptible to the impact of iodine than others. But it is not a simple subject.
And you might care to consider the questions over casein - but maybe almost anyone else knows more than I do about that.
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