I am in an MPH program where we take comprehensive exams (only MSPH students write theses), so in terms of research, advisors are not expected to guide you as they would a PhD student. Because there are no expectations placed on the advisors, or formal processes like thesis-writing to frame a closer relationship, it depends on the advisor. It helps a lot if you take their classes and/or if they are willing to guide you in independent study. If they have research assistantship opportunities where you can help them with their research, even better. My advisor happens to teach a lot and be very welcoming and open. Still, she advises many other students... I don't know of any advisor in my program who is going to come after you to check-in and see if they can support you with research--its up to the students to develop this relationship!
Also, because of the very little obligation that advisors have to students in my program, we are very free to seek out more helpful professors without really needing to make a formal change in advisors.
Perhaps other MPH folks who have to write a thesis have different experiences...