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You’re looking at a content-based recommendation algorithm. AFAICT StackOverflow’s looks at the tags and the words in the title, and finds questions that share some of these. It can be implemented as a nearest neighbour search in a space where documents are represented as TF-IDF vectors.
Implementation-wise, go with any Django search engine that supports stemming, stopwords, non-strict matches, and tf-idf weights. Algorithmic complexity isn’t high (just a few index lookups), so it doesn’t matter if it’s written in Python.
If you don’t find a search engine doing what you want, leave the stemming and stopwords to the search engine, call the search engine on individual words, and do your own tf-idf scoring with a score that favors similar tags.