I first visited Santiago de Compostella in 1989. I witnessed women doing the laundry in a communal trough in the middle of the street in a small village only a few miles outside the city. SdC itself was a provincial backwater with a magnificent, if slightly neglected, cathedral, and pilgrims were very few and far between. It was obviously poor compared with, say Barcelona or Valencia.
I returned a few years ago, and I agree with Kanga that it has changed immensely. Although some of this is undoubtedly drug money, a major change has been the attitude of the Spanish government. In Franco's day, the Galician language, like other regional languages, was outlawed (strange, as Franco was a Gallego himself) and investment in the provinces (not just Galicia) was almost non-existent. Galicia did not benefit from the tourist boom enjoyed by the Mediterranean Costas, but SdC is now a major university city and the region as a whole does well out of fishing, agriculture and tourism as well as some industry. (There is a Citroen plant at Vigo.) Spain's accession to the European Union, with its emphasis on regional and marginal assistance, in 1986 undoubtedly helped to boost the local economy. And, of course, the Camino is now a considerable source of income.
It is certainly as safe as any where in Spain, and probably safer than Barcelona or Madrid.