We don't really understand viruses that well. Viruses appear to have many tricks up their sleeves, including air transmission. Earth is full of viruses (thousands upon thousands), many of which we do not yet understand or even know exist. We could certainly develop (consciously or accidently) a bio-weapon that changes how they behave too. If we ever meet a civilization, we're not just going to say "hello" and then go our separate ways. We're going to come in close contact with them, their animals, and technology. This close contact increases the chance of cross-contamination. The chances are very high that they could introduce a virus into our ecosystem or we could introduce a virus into theirs. An alien virus is perhaps the biggest threat we face from a non-hostile alien civilization.
You bring a good point. If we stay apart, then the chances are small because of the distances involved. But let's consider the following scenario. An alien civilization uses FRBs to communicate with us across a vast distance. They teach us how to create an "FRB 3D printer," so we can share information. A malicious civilization could use this FRB 3D printer to send a virus across vast distances without having to set foot here. This would be a good way to transform our planet and invade it at a later date.
There is no guarantee that alien intelligence is similar to ours, so there's no telling what they would do. But let's use human intelligence as an example. Humans are very adventurous and wreckless. For example, we know that there could be dangerous viruses on Mars (if there's life), and yet we're only a few years away from going there in spite of this danger. We'll be digging around in no time. Closer to home, we know that bats and other creatures carry viruses, and we're still poking around in caves. We also know that there could be viruses in frozen lakes in the arctic, and we continue to dig up and bring up life from its icy depths. So, in spite of the danger, we continue exploring and touching other life-forms. A sufficiently advanced civilization may also decide to come poke around on Earth for research purposes.
We are already capable of creating organisms using synthetic DNA. In a few decades, this will be routine. So, a sufficiently advanced civilization (several hundred, thousands, or millions of years ahead of us) could do it fairly easily. We now know that FRBs are capable of carrying more complex information, so if we use them to communicate, we could send complex instructions to each other. You're right that they might not understand our nervous system, but if we share that information then it will be easy. Because of our social nature, humans like to share too much information. Here's exhibit A:
We even put our home address!