Are hot springs in non-volcanic areas radioactive?
The answer is contained within your own question. Virtually everything is radioactive, including your own body, the air you breathe, and everything you eat. The radioactivity is usually beta radiation (emission of energetic electrons), which is the least harmful form of radioactivity. 

Radon gas, which is emitted from granite rocks containing uranium, sometimes builds up to dangerous levels in our homes and is an alpha emitter. Alpha radiation is very ionising and dangerous, but needs to be ingested into the body to cause serious harm.

The answer to your question, therefore, is yes, hot springs are radioactive, but so are cold springs. As hot springs are more likely to have passed through granite rocks, they are probably on average more radioactive than cold springs, but neither are radioactive enough to cause concern. 

The radioactivity which is dangerous enough to cause concern is radon gas, which varies from place to place according to the underlying rocks. Maps of radon hotspots can be obtained from the internet. If you happen to live in a hotspot, you need to keep your house well ventilated, otherwise the radon will build up to dangerous levels, sometimes levels which would not be tolerated in a nuclear power station or research establishment.