Verizon Fios allows it, AFAIK. The fiber terminates inside the house and converts to coax. Apparently there's an ethernet port on the fiber modem and you can skip the coax entirely if you just need ethernet.
AT&T's network uses 802.1x authentication and the client certs are burned into ROM on the router.
The router has a crappy passthru mode where it gives your own device the external IP and sends any traffic to it, but under the hood it maintains its own (rather small capacity) NAT table for all the traffic. There's not a real bridge mode.
Some more technically inclined folks have come up with solutions like a proxy that just forwards 802.1x traffic to the router so it can respond, or rooting the AT&T box and pulling the certs out of ROM so you can use them to auth on your own network device.