If RabbitMQ attempts to start but fails, the reason will be shown in its output (e.g. "journalctl -eu rabbitmq" or whatever the service name is).
One guess is that RabbitMQ is trying to bind to the same port as prometheus. Prometheus uses port 9090 by default, and I think RabbitMQ uses port 5672 and 15672 by default, so they ought to be fine. But maybe there's some additional port configured in one or the other.
If there's no attempt even to start RabbitMQ while Prometheus is running, then this would be down to your process manager (e.g. systemd); maybe systemd has some weird dependencies configured between those two packages? This would be unusual.
Those are a couple of ideas, but basically this is a problem with your system which you'll need to resolve locally. The best practice in any case would be to run Prometheus and RabbitMQ in separate VMs, or at least separate containers.