Yes, the URS is secure, at a number of levels. First, you may notice the "https" in the URL: https://earthdata.nasa.gov. That tells you that when you're talking to URS, you're talking over HTTPS, the secure protocol for communicating over the network. Second, your password is encrypted in URS. That means that even URS administrators can't simply open up your record and check out your password–even from the back-end! And third, because when you log into EOSDIS tools and services, you use a form provided by URS itself, you're never giving your password to another application... even one you trust!
In addition user information will never be sold to commercial providers or shared with other government agencies.