I would recommend that you publish the project to a SharePoint site, this would allow users to view, update and manage their tasks assignments. As they updated their tasks, then you could interface with the site and update your project. SharePoint is available on a Mac and they would not have direct access to the MS Project file. No need to load anything on their machines or yours. MS Project 2010 has this functionality built into the product.
If you are on an earlier version of MSProject or need additional functions their is an add on tool called Project Publisher, which can be purchased from the following link.
You can read more about it at this link: https://www.myepm.net/SitePages/Home.aspx or purchase at the following link https://www.plimus.com/jsp/buynow.jsp?contractId=1711030&referrer=PMProviders' defer='defer