You could have a series of drop-down lists containing field names. Each drop-down list could be separated from the next by a pair of fixed-choice buttons setting "OR" or "AND" between the lists. Where it gets tricky is that you may want the user to be able to use brackets around some of their selections.
Does someone know if their are "plugins" for Django to get a type of filtering on the models like the "advanced" filter options on the Bitbucket issues page or even "more advanced" like pubmed? This last one can also do the "bracket-option". I would think this is a quite common feature needed, but I can't find anything. It might be I'm searching with the wrong terms.