I'll try to just directly answer the question of "What should I do?" ('about my advisor getting involved in something I consider pseudo-science')

• If its important enough, talk to them.
  • Polite conversation about the motivations and interest in the subject while trying not to start the conversation with "I'm obviously bias and view this as bad"
  • Segway into personal concerns (whatever they happen to be).
    • If you're going to dive into "I'm concerned about you, and what this might do to your career" then treat the topic with some care. Like some answers have noted, many folks will often take that approach as rather pretentious.
    • If its "I'm concerned about your new research will do to me" then make sure you have a pretty good idea about what the supposed risk is. Research has to be pretty bad to completely torpedo the value of recommendation letters from someone with a long track history in a field.
    • Reason I start with "have a polite conversation that's mostly curiosity and attempting to understand the situation" before diving into recommendations or concerns.
• Read about the subject critically.
  • Is it all pseudo-science?
  • Are there possible research avenues that might be valid or might simply not have been explored?
  • Is there some issue with "accepted" approaches that's causing people to look for alternatives?
    • Ex: "We Hate chemotherapy and how it makes us feel, is there any other choice?"
    • "Why yes there is" says the Mayo Clinic and Medical News Today.
      • You can try acupuncture, aromatherapy, hypnosis, meditation, music therapy, ect... to try to deal with the symptoms.
      • You can try photodynamic therapy, laser therapy, immunotherapy, targeted therapy, or hormone therapy to try to deal with the tumors.
• If its still bad after these, finish your PhD, without souring your relationship.
  • Do quality work you can be proud of
  • Have publications, references, and other support for your future life so you're not totally dependent on a recommendation from your advisor
  • Let your advisor worry about their own career (unless there's some "serious" ethical / legal issues)

I'll try to just directly answer the question of "What should I do?" ('about my advisor getting involved in something I consider pseudo-science')

• If its important enough, talk to them.
  • Polite conversation about the motivations and interest in the subject while trying not to start the conversation with "I'm obviously bias and view this as bad"
  • Segue into personal concerns (whatever they happen to be).
    • If you're going to dive into "I'm concerned about you, and what this might do to your career" then treat the topic with some care. Like some answers have noted, many folks will often take that approach as rather pretentious.
    • If its "I'm concerned about your new research will do to me" then make sure you have a pretty good idea about what the supposed risk is. Research has to be pretty bad to completely torpedo the value of recommendation letters from someone with a long track history in a field.
    • Reason I start with "have a polite conversation that's mostly curiosity and attempting to understand the situation" before diving into recommendations or concerns.
• Read about the subject critically.
  • Is it all pseudo-science?
  • Are there possible research avenues that might be valid or might simply not have been explored?
  • Is there some issue with "accepted" approaches that's causing people to look for alternatives?
    • Ex: "We Hate chemotherapy and how it makes us feel, is there any other choice?"
    • "Why yes there is" says the Mayo Clinic and Medical News Today.
      • You can try acupuncture, aromatherapy, hypnosis, meditation, music therapy, ect... to try to deal with the symptoms.
      • You can try photodynamic therapy, laser therapy, immunotherapy, targeted therapy, or hormone therapy to try to deal with the tumors.
• If its still bad after these, finish your PhD, without souring your relationship.
  • Do quality work you can be proud of
  • Have publications, references, and other support for your future life so you're not totally dependent on a recommendation from your advisor
  • Let your advisor worry about their own career (unless there's some "serious" ethical / legal issues)