Can the Garmin Edge 130 obtain heart rate from a fitness wrist-band?

GPS-based computers, which are often called head units, typically use two communication protocols: Bluetooth (which is the same as many personal electronic devices like smartphones use) and ANT+, which is a protocol developed for the cycling world. I think that ANT+ was initially developed for power meters, but it can be used for other devices.

Correspondingly, many of the things you might want to connect to a head unit broadcast data using either or both ANT+ or Bluetooth. You can very often connect any brand of device to any head unit if they both have ANT+ or Bluetooth. ANT+'s own page lists a set of devices that have ANT+ and that are known to be compatible with the Edge 130. Obviously, Garmin's own heart rate straps are compatible, but straps from Garmin's main competitor Wahoo, as well as Bontrager, Timex, Tacx, and a number of brands I don't recognize are compatible as well. In general, if the device you want has either ANT+ or Bluetooth, it's very likely it can pair with a head unit.

However, the question refers to fitness bands, which I would assume means watches like Fitbit. One of the exceptions to the above rule is with these items. As @AdamRice noted in comments, the Apple Watch and the Fitbit can read heart rate data themselves, but they will not broadcast it to head units. They have the hardware to do so, but the restriction is in their operating systems, and this can't be changed by the end user. The ANT+ page I linked to listed many Garmin watches as compatible with the Edge 130 (and most likely with other head units), but these watches were clearly designed such that head units can see them as standalone heart rate sensors.

Many smart watches may be able to pair, at least in theory, with cycling sensors. With the Apple Watch, someone would have to design an app for this. Thus, in theory, I could connect my Quarq power meter to my Apple Watch via Bluetooth, if I or someone else were willing to write an app. This is akin to treating a smartwatch like a head unit.

Just for interest's sake, what are some of the more unusual things you could connect to a head unit? You can connect tire pressure sensors, as described in the comments on this question - some gravel racers use them, but they are expensive. You can connect muscle oxygen sensors, which are thought to be another way to measure effort. People with electronic shifting systems can often connect the system to their head unit, and thus gain a gear display. You can connect smart trainers, which enable you to do virtual cycling. The Edge 130's compatibility page lists the Kayak Power Meter, which is obviously a power meter, only for the sport of kayaking - although I'm not sure that I'd go kayaking with an Edge 130 head unit. Several companies make smart lights that broadcast over ANT+, but only Garmin has implemented this protocol on their head units. Thus, Garmin head units can control smart lights, while Wahoo head units can't. Apparently, the ANT+ light protocol is not a straightforward thing to implement. Garmin makes a rear-facing radar that detects and alerts you to cars behind you, whose ANT+ protocol several companies apart from Garmin have recently implemented - hence, until late 2019, only Garmin units could control their Varia radar, but now Wahoo and at least one other company's units can do the same.