Yes. As the price goes up, people switch to non-meat protein. Similar to what is hopefully going to happen with fossil fuels and renewable energy.
A lot of the foods have already had these nutrients destroyed through processing (to resist more time on the shelf) or genetic modification (to increase yield, etc). It's part of what's leading us to higher and higher numbers people with chronic diseases, cancers, etc.
We'll see more of that as we give up "natural meat", too.
Most of the folks who are, say, antivaxxers firmly believe that metals, pesticides and other chemicals are a primary cause of chronic illness. The reality is that chemicals of that sort concentrate in fat stores in animals and get worse the further up the food chain you go.
It is one of the better arguments for eating vegetarian.
The woo part in the GP’s comment seems to be a hidden implication that animal meat is not processed or hasn’t had its nutrition destroyed or not been genetically modified or not been fed “pills that people are skeptical of”. There’s almost nothing “natural” about animal meat that’s sold in stores. And hence the conclusion that some disorders would increase solely because of this is false.
The technical term for your description of the concentration of certain things increasing up the food chain is “biomagnification”. [1]