
You need to use their modem quite often, but you don’t need to use their router. They’re usually “all in one” modem/router things these days, but they’re legally required to provide you with a modem in bridge mode if you ask — at that point, an Ethernet cable attached to their modem is effectively attached to the Internet, and you can put your own hardware inside (firewall, Wifi router, etc.).
While you need to connect to their IP gateway, you don’t need to use their DNS services or anything but their IP gateway service.
Bridge mode disables the router in the modem; if you have an admin account on the modem you should be able to enable it yourself; otherwise you need to get your ISP to enable it. It will turn off all the firewall and WiFi features on the modem.