To be honest I really don't recommend it. With RW, they will force you to join any nearby Wifi network - even if it requires you to accept its ToS and you haven't done this. So if you are waiting for Amtrak and the opposing train pulls up for 2 minutes, you are switched onto this network. Or if you are in a bus on the highway in traffic and you pass a Wifi hotspot, it will switch you onto it... Even if you turned off Wifi. It constantly turned on Wifi even when you explicitly tell it not to. Google Fi has not done this so far. And, if the public Wifi requires me to accept some ToS, Google Fi will keep me on 3G until I have accepted the ToS and am /actually/ on the internet via the public wifi. So, in the end, RW really pissed me off. Still, it is a cheaper service and as a college student it was all I needed. I stayed on one network 24/7 and had no complaints at the time.
Edit: One thing about being forced to switch to a network is that it is silent and you don't necessarily know if you are connected to the internet or not. So if you walk into a Starbucks that has public wifi and your wifi is turned off, your wifi will be turned on and you will have no internet connection until you accept Starbucks' ToS. This has left me very confused before missing messages, calls, etc.
I'm confused. I've been a Republic Wireless customer for about a year now, and I've never noticed any pressure to use an open network. My home network is the only wireless network to which my phone will automatically switch. When I'm away from my house, I remain on 3G unless I explicitly choose to connect to another network. It will attempt to reconnect to a network that I've used in the past, but one can stop this by 'forgetting' the network in Android settings.
Maybe I have a different phone? I'm using a 3G Moto G. Maybe I turned off something in settings? I have not rooted the phone, but certainly may have changed something from the standard settings menus. Here's someone else agreeing that your Republic Wireless phone should never connect automatically to a new network: https://community.republicwireless.com/thread/26466
I think you were either experiencing a bug that has since been fixed, or you were running some other app that was automatically approving the connections (like Wifi+). I would not discourage anyone from using Republic Wireless due to this worry. At least currently, you are never forced to use any wireless network that you do not want to use.
As jerf mentioned in the sibling comment, it appears my experience is not representative. I also had the Moto G, first generation? I had it for about a year and a half. Maybe I screwed something up in my settings too. I definitely would love to have had a different experience! I can't comment on why the things happened as they did. But for whatever reason on my phone I definitely had a bunch of issues. Maybe there was an issue with the radio hardware on mine? Not sure.
Edit: One thing about being forced to switch to a network is that it is silent and you don't necessarily know if you are connected to the internet or not. So if you walk into a Starbucks that has public wifi and your wifi is turned off, your wifi will be turned on and you will have no internet connection until you accept Starbucks' ToS. This has left me very confused before missing messages, calls, etc.