GPS devices only receive GPS signals; they do not broadcast any data. So carrying a basic handheld GPS device won’t give away your position to anyone else. However, a smarter device like a phone or InReach emergency locating device can relay your location to others.

For communications, lots of people would suddenly get really interested in VPNs and encryption (for using the existing Internet), private wireless mesh networks (for city- and region-level communication), and even amateur radio. Owners of mesh nodes or radios would need to limit their broadcasting time and/or do a lot of moving around to avoid being located.