Then first off you won't need a Bela cape.
You'll need just a SBC (single board computer, such as BeagleBone Black, Raspberry Pi, or something with two ethernet ports on board, such as the AM62-SK) or even a microcontroller (not sure which ones have two native ethernet ports). Getting good timing out of these general-purpose devices depends on how you define "good". If latency and jitter of the order of a handful of ms or more are fine, you can use basically whatever on the SBC side. If you need anything tighter, you may need some custom real-time kernel if using a SBC, or use a microcontroller.
If using an external network switch or a USB-ethernet adapter is an option, then removing the dual-ethernet requirement broadens your choices significantly.