As somebody who has done both, there's certainly a lot of similarities in how you write software.
I'm talking about real-time audio, though. There's also just audio playback (Pro Tools, e.g.) which tolerates much higher latency, but enables higher audio fidelity due to larger buffer sizes (e.g. in compressors to enable look-ahead) as well as more clever algorithms (which are often prone to latency spikes, such as a "standard" FFT, if you want a very simple example).
Both, finance and real-time audio, differ in their time scales, but more in the breadth of their time scales: real-time audio is often between 1–50 ms (yeah, we try to keep it below 10 ms, but that's tough to do in a complex setup. I've seen artists often compromise and increase buffer sizes (== latency) to accommodate for their complex virtual instruments and filters), finance in ns–ms (it's not HFT anymore at a certain point, sure, but those HFT architectures also have a layered response, with FPGAs being quick but simple and more complex strategies having higher latency; also, if you're e.g. asked for a quote on a bond, it's not a shame to take 500 ms to think about a price, because those trades are bigger but slower).
You also mentioned the consequences of missing a deadline. Well, indeed, I've seen this variance to be less of an issue in finance (we're only caring about xx µs, so I hesitate to call myself a HFT guy) than in real-time audio. A click in a live set is a no-go. A crash of your DAW is fatal, that's it with your live set. Nobody dies, but people will be very upset. I've seen real-time audio being obsessed with being reliable and keeping the variance in latency really small.
In finance, I've seen it more that people kind of accepted that variance was huge because there's some hidden allocations in a system. Hoping that those stop once the system is warmed up or that they rarely occur on a critical trade.
As a side note, in finance I've even heard this well-known HFT firm: "Well, it's not the end of the world if your process crashes. If you can restart quick enough."
It's also that in finance, your data is more heterogenous: Real-time audio has audio (isochronous, homogenous buffer of floats), MIDI (asynchronous, formerly small events), parameter changes (asynchronous, often just a float) and config changes (changes the topology of your audio processing graph; enjoy to transition from A to B without causing an audible glitch). Finance has processing graphs that only process asynchronous data (heterogenous market data, telling you what's on the order book of an exchange; trade data for which trades you performed with your orders and quotes; symbol data when new securities appear or change (historically only with the start of the trading day); pre-computed steering data for algorithms and/or data from third-party data sources).
Thus, the processing graphs of both differ in the data that's transferred as well as in the structure and domain. In finance, there is no regular tick-based processing. You have to accommodate a very varying amount of data per time period, whereas in audio, it's a very regular pace and the amount of data is often the same (± activations of voices in instruments).
Real-time audio has plugins, though. And those, from experience, do whatever you can imagine. Plugins are great, from a creative perspective, but the craftsmanship is of very varying degree. I bet I'll even find a plugin that draws the UI from the real-time audio thread.
Any other experiences from the real-time realm?