Different organizations have different policies about their data. These policies are driven by both laws and organizational policies and often relate to confidentiality agreements with subjects. Therefore, there is no single answer to your question. My advice is to build a relationship with individual authors of articles that use data in which you are interested. Most authors are willing to share data with other legitimate researchers if it is not restricted by law or policy. Some even attach data sets to Researchgate posts. You might email an author with a general question. You might even request to participate as a coauthor. As a relationship develops, ask about data sharing. Good luck!
US government data that's available. We have https://www.data.gov/ that is surprisingly robust. Also the BLS, Census, OECD, and World Bank open data https://data.worldbank.org/ have much more social issue related data than you might expect
Search for papers on the subject of interest and ask the authors for their data/sources
Many companies and cities are now open sourcing their data so that people can help solve problems. There are also non-profits doing this. One example is http://www.datakind.org/. Many nonprofits will give you data in return for help with analysis.
Some datasets are available to students/researchers that may not be available to those in industry