I presume you're talking about the regular fleetships, but if you're not...
Spirecraft (asteroid types)will only be sent against you on Spirecraft Hard, or as some other high budget - which is usually a hard minor faction.
Spire vessels (as in dreadnaught, battleship, frigate) can be avoided simply by not selecting the "Spire Hammer" AI.
Spire Corvettes are a bonus ship type, rather than related to any faction and there isn't much you can do about them, though I don't remember ever seeing the AI with them.
Spire champions (or Nemesis, to be exact) will only show up if you have a champion yourself.
Otherwise, some careful selection of AI types should minimize the spire that show up. The clearest solution is to pick an AI with another theme, such as the Zenith Descendant or Neinzul Youngster, though that won't guarantee anything. A lot of the easy AI types aren't particularily skewed towards spire ships either, but there are a few moderate and above types that are extra rich in spire ships.
Stealth Master, Shadow Master, Extreme Raider - Spire Stealth Battleships
Feeding Parasite, Teleporter Turtle - Spire Teleporting Leech
Spireling, Spire Hammer - see name
Thief - Spire Tractor Platform
If you're looking to avoid spire ships, I also recommend turning off all Swallower types. Unlike disabling stealth, gravity effects, or tractors, it shouldn't have an impact on core strategy.
