Protected from competition, no. Protected from unfair competition, yes. There are a limited supply of taxi medallions in NYC (~13,000?), the number of which is controlled by the government, and getting one (last I saw) will cost you upwards of a million dollars.

Uber is basically coming in, running a taxi business, and refusing to pay for the government mandated barrier to entry. I'm not expressing an opinion on the system as a whole, but I think it's hard to deny that taxi folks (from the drivers up to the people that own the medallions) have a valid reason to complain.