How can I protect open research from being plagiarised?
Use a license.

Different open science journals/repositories/etc. allow you to license your publication(s)/data/etc. Some allow you to choose a license; others do not. Others may have different repositories.

For example, arXiv gives submitters a licensing choice:


  arXiv does not ask that copyright be transferred. However, we require sufficient rights to allow us to distribute submitted articles in perpetuity. In order to submit an article to arXiv, the submitter must either:
  
  
  grant arXiv.org a  non-exclusive and irrevocable license to distribute the article, and certify that he/she has the right to grant this license;
  certify that the work is available under one of the following Creative Commons licenses and that he/she has the right to assign this license:
  
  
  Creative Commons Attribution license (CC BY 4.0)
  Creative Commons Attribution-ShareAlike license (CC BY-SA 4.0)
  Creative Commons Attribution-Noncommercial-ShareAlike license (CC BY-NC-SA 4.0);
  
  or dedicate the work to the public domain by associating the Creative Commons Public Domain Dedication (CC0 1.0) with the submission.
  


The Royal Society Open Science journal has a different policy:


  All papers are made freely available under an open access model immediately on publication at the Royal Society Open Science website and are deposited in PubMed Central on behalf of the author. Under a Creative Commons Attribution License (CC BY 4.0), authors retain copyright for their article but allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles provided the original authors and source are cited.


Once a license is chosen, all that remains is to enforce the license, which is simple enough. License enforcement is up to the holder of the license. If you choose the first of arXiv's options, then the responsibility is arXiv's; if you license the work under one of the Creative Commons licenses, then the responsibility is yours.

The enforcer of the license general is not required to enforce it if he/she/it so desires (see Are you obliged to enforce your license? on Open Source for more information, although that covers the GPL license, which is not applicable here). It's typically in the best interests of the license holder to enforce the license, but there is no requirement. If you want to make sure that the license is enforced, then you would be best off keeping the license yourself.