If you want to be rigorous, there's no easy answer to your question.
For starters, SSR's will create a lot less voltage "jumps" (sorry, I don't know the right English word) than mechanical relays or contactors, as they have a smoother ON/OFF transition.
That said, the real cause of those voltage jumps is much more complex that just the type of relay you're using. Contrarily to what most people think, wires are not just resistors. A wire is a resistor with a coil in series, and several capacitors between it and other wires, ground, etc. What that means is that a wire has inductive and capacitive components, that are related to its length, diameter, distance to other wires, ground, walls, etc. All of that will make the wire act like a filter, showing a differential attenuation for different frequency disturbances. Add to that that the transformer that feeds your house also has inductive (of course) and capacitive components, and you can see how complicated it can get.
Bottom line, if you're an electronics engineer, with LOTS of time on your hands, and you happen to LOOOOOOVE math, maybe you can calculate it. Other than that, the only accurate way to know the amount of variation produced by your SSR's switching would be to hook up a digital oscilloscope to the line, and run your machine. So, if you have, or know someone who has a digital oscilloscope, you can try it. Otherwise, I wouldn't worry too much. Most appliances are pretty resilient, and the sensitive ones will start functioning erratically way before they crap out on you.
One test you could do would be to hook up a desktop PC right on the same outlet (or as close as possible) your brewing setup is plugged into. If you see the PC acting weird when you're brewing, you should look for a solution. If the PC works fine, you're OK. Just make sure it's a DESKTOP, as laptops are protected by their battery.
Finally, if you see some of your appliances starting to act crazy when you're brewing, a couple of fairly cheap solutions to your problem would be to minimize the length of common wire between your appliances and your brewing setup (meaning, putting your setup on a dedicated circuit, right off the house main breaker), and, if that doesn't solve it, getting an isolation transformer for it.