I would say, whether you're a scientist or not, your obligation to take seriously ideas that are extremely unorthodox (like Homeopathy) depends largely on your role in relation to the unorthodox idea.
If you are a medical doctor who serves patients, you probably can't be reasonably expected to spend your time vetting every possible wacky idea. It's infeasible to expect every doctor to do this, so these doctors ought to mostly focus on the proven-effective treatments and largely ignore the more wacky ideas.
If you are a reviewer in the peer-review process, however, you probably ought to take seriously every paper you've been asked to review, at least for long enough to give it an honest review.
Not everybody can afford to take every idea seriously, we have limited time here and some ideas have been given more time than they deserve already.