TL;DR: you're getting the wrong meaning of "obscure".
You seem to be assuming that "obscure" means something like "strange" or "difficult to understand", but the more common (in my experience) meaning of the word is something more like "unknown" or "not famous". Indeed, the Cambridge English Dictionary lists two meanings:
obscure adjective (NOT KNOWN)
not known to many people:
an obscure island in the Pacific
an obscure 12th-century mystic
obscure adjective (NOT CLEAR)
not clear and difficult to understand or see:
Official policy has changed, for reasons that remain obscure.
His answers were obscure and confusing.
This makes more sense in terms of the character of Jude: he spends so much time trying to enter into one of the colleges of
Oxford Christminster, to achieve an education, to study theology, even to become an academic clergyman, but in the end he remains a stonemason and labourer, his obscurity in the world upper-class academia guaranteeing his rejection from every college he approaches. In the end he dies unknown, unheard of, without qualifications, none of his dreams achieved - in a word, in obscurity.
There's even one passage in the story where the word "obscure" is used by Jude himself, in reference to his and Sue's divorces. It's a throwaway usage of the word, not hugely significant, but it emphasises the point that poor people such as they are considered "obscure" by society, not worth paying much attention to:
The same concluding incident in Jude’s suit against Arabella had occurred about a month or two earlier. Both cases had been too insignificant to be reported in the papers, further than by name in a long list of other undefended cases.
“One thing is certain, that however the decree may be brought about, a marriage is dissolved when it is dissolved. There is this advantage in being poor obscure people like us—that these things are done for us in a rough and ready fashion. It was the same with me and Arabella. I was afraid her criminal second marriage would have been discovered, and she punished; but nobody took any interest in her—nobody inquired, nobody suspected it. If we’d been patented nobilities we should have had infinite trouble, and days and weeks would have been spent in investigations.”