a) Inductive Logic Programming (and generally relational learning) is ideal for feature discovery and firmly in the symbolic camp, so the reliance of the Symbolists on hand-crafted features is not an absolute.
b) PAC learning should go under symbolic techniques, no? In fact, so should decision tree learning.
Also, I think it's obvious you can always unify and divide classifications like the above to come up with as many or as few "tribes" as you like. The real question is: are there really that many people who are wedded to their favourite technique, so much so that they won't ever try anything different?
b) if we apply hierarchical clustering, it would probably be a subset.
Anyway, this was more or less tongue-in-cheek. And yes, you could go on and on. I should have added "The Logicians", "The Game Theorists" and the NLP'ers solving object detection problems with visual bag-of-words. Also forgot to take a jab at business intelligence/operations research.
As for being wedded to a favorite technique, I think that is largely a problem for beginners (and PhD. students with a supervisor who can only think from within a certain framework). I myself may try SVM, but I rank it pretty low as an alternative.
Anyway it depends a lot on the specific algorithm, for instance see Alignment-Baed Learning  and the ADIOS algorithm  for two examples of thoroughly symbolic grammar induction algorithms (though not quite ILP) that works on unannotated, tokenised text, so is entirely unsupervised.
And, if I may be so bold, my own Masters dissertation , an unsupervised graph induction algo that learns a Prolog program from unannotated data. You won't find evidence of that on my github page, but I've used my algorithm to extract features from text- as in word embeddings. Also, it's a recursive partitioning algorithm, so essentially an unsupervised decision tree learner, only of course it learns a FOL theory rather than propositional trees. My hunch is you could use decision trees unsupervised and let them find their own features, although that'll have to go under Original Research for now :)
Those just happen to be three algorithms I know well enough, but you can google around for more examples. In general: relational learning can do away with the need for feature engineering, it's one of its big strengths.
In fact, I'm starting to think that - unless DL is somehow magical and special - it should be possible to turn most supervised learners into unsupervised feature learners, by stringing together instances of an algorithm and having each instance learn on features the previous one discovered. Again- Original Research and big pinch of salt 'cause it's just a hunch.