If it makes you feel better that you are "doing something" by replacing your shower head, then do it. But that doesn't help with exposure to MAC prevalent throughout the environment.
After reading everything I can get my hands on, I would say the science isn't there yet to prove a conclusive link between your MAC infection and specifically, your shower. And even less that replacement of the shower head will "cure" the problem or prevent reinfection. As I understand this disease, once your lungs are colonized with MAC, it is not totally eradicated by treatment - just knocked down to undetectable numbers, so trying to "prevent infection" may be a moot point.
All of the studies cited are of very limited scope, with small sample sizes, and only one (from Japan) compared strains of mycobacterium found to the strains infecting residents of the homes. The results showed that only a few of the NTM found in the showers matched the strain the patient was infected with. None of the studies went as far as to evaluate any treatments like disinfecting or replacing the shower heads.
From a microbiological perspective, the biofilm that is formed surrounding NTM is tough, and I don't know what you can do at home to dislodge it & disinfect. That should certainly be subjected to thorough study as part of NTM research. That biofilm readily attaches to plastic - hmm, maybe the increase in infection is linked not to the shower heads, but to the replacement of copper plumbing and metal fixtures with plastic fixtures and pipe (PVC & PEX.) That would certainly be something to study as well.
As for myself, I have chosen to take the path of living a normal life, with reasonable precautions. I eat, rest, exercise, take my meds and do my breathing treatments to stay healthy. I wash my hands (a lot) and keep them away from my face. I avoid close contact with sick people. That means taking care when handling soil (avoid dust, wear gloves, wash thoroughly afterward.) At my Texas home, where I am pretty sure I contracted MAC, I have covered all the soil near my patio with ground cover, have a gardener mow, weed, rake & fertilize my yard & wash the patio while I am away & the house is well closed. I only garden there in pots with sterile potting soil. And I avoid blowing dust.

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