Should I complete a master's thesis if I intend to move to a different graduate school? I'm currently a first year graduate student in mathematics in the United States. After having completed my requirements for a master's degree, I'm considering moving to a different program, based on reasons I outlined in a previous question. 

My question should one necessarily work on a master's report/thesis to boost one's application to enter a different PhD program? 

I can probably get a master's degree without having to write a report/thesis as I have already passed some of the qualifying exams at my school. 

So, to what extent would having completed a master's thesis help me in switching programs? My interests are a bit broad, and interdisciplinary, so I'm, as of yet, broadly interested in a couple of areas, and not a single, specific area of research. So, I would like to apply to schools that have research groups in at least 1-2 fields of my interest.  

Any suggestions on how graduate committees in math or STEM fields view the issue of masters thesis or reports.
Since the doctorate is about research, having some solid evidence of doing that successfully is a plus. You can change your main focus to another subfield after writing a master's thesis, so don't worry that it will limit you. 

But my main question back to you is what you will be doing in the meanwhile if you don't do the thesis. Will it be at least as positive an influence on admissions committees and potential advisors? It seems doubtful, but possible, depending on your situation. 

An MS isn't really required for admission to the PhD in the US, but a positive record that predicts success certainly is. Do whatever you can to build that record.