how early do you need to arrive at the airport or port when traveling
between islands?
For domestic flights, at Athens and Santorini airports plan to arrive 1h to 1h30 before the flight.
Note that with Aegean/Olympic or Sky Express, using their apps, you can check in 48 hours in advance and get your boarding pass on your smartphone
About the ferries, plan to be at least 30 minutes at the port before the arrival time of the ferry.
Anyway they are rarely on time except early in the morning when the ferry starts its journey. In this case you can be at the port 1 hour before and board the ferry.
Don't worry too much about the ferries and as Lee tells you, favor the traditional ferries (Blue Star Ferries type) with which you feel less confined than with the fast catamarans like the Seajets.
When I go island hopping in Greece I always watch the weather forecast. In particular wind forecasts on:
https://meteo.gr/index-en.cfm
(click on Greece, Cyclades and choose the island)
From 7 or 8 Bf wind force with strong gusts on the day you have to take the ferry, there is a risk of cancellation or severe delay.
Above 8 Bf it will most likely be a sailing ban for all ferries, even the traditional ones