Is citing a blog post allowed in a research project?
This is fine. Citing someone's opinion is different from reusing someone's results as long as the former is clearly separated from the latter. Find a way to distinguish both kinds of citations in your essay. The former is the data on which you operate, after all. 

If your advisor insists of such a separation, consider using footnotes, endnotes, or an extra list (in addition to the bibliography).