Ion cannons let's the second player place the objective tokens after deployment, but spynet redeployments also happen after deployment. Which happens first? Can the first player redeploy to avoid the ion cannon?

No; if two effects belonging to different players share the same timing, the first player resolves all his effects first.

Does it matter that it is an objective effect and not a player effect? Because the rules reference talks about the if both "players have effects" then the rule you mentioned occurs.

2 hours ago, NightAngel47 said:

Ion cannons let's the second player place the objective tokens after deployment, but spynet redeployments also happen after deployment. Which happens first? Can the first player redeploy to avoid the ion cannon?

EDIT: Sorry, I erased my first response as you were referring to the Base Defense objective, but I confused it with the Planetary Ion Cannon objective.

In that case DiabloAzul is right, the first player must resolve all of his effects. Although is from an objective, the placing of the tokens is an effect that must be resolved by the second player

Thanks for the responses!