Setup I am using in case you are not sure what I mean.

Can not reproduce.

Using the provided blueprint. setting both manually to "target missiles" and "turret", both work and shoot at missiles, settings get not changed. Activating the AI in the structure tab activates only the last turret on the chain but that is not the issue here.

The issue is not that either of the turrets fail to shoot at missiles, but that the middle of the chain acts like it is using the "All" setting for targets. This results in the end of the chain firing at missiles, and the middle of the chain firing at ships FIRST in a combat situation.

In T553#19550, @33Cav wrote:

The issue is not that either of the turrets fail to shoot at missiles, but that the middle of the chain acts like it is using the "All" setting for targets. This results in the end of the chain firing at missiles, and the middle of the chain firing at ships FIRST in a combat situation.

I did try that and spawned in pirates, both parts stayed in the shoot at missile setting in my tests.

I have retested
Steps to reproduce
-Set end of chain as follows "Turret, Missile, ON"
-Set middle of chain to "Ship, Missile, ON"
-Watch as the middle chain shoots pirate ships that don't even have missiles

Works best on ships without missiles.

To my knowledge the combo:

Ship and missile do not work.
If you class a part of the chain as "ship" its designated to engage enemies on its own, as it "thinks" it is a ship.
So, if the entity set to "ship" does not respond to the setting of a child turret, its a design flaw, but not a bug.

So, as a result we may want to deny the use of "missile" for "ship", but this may flip the setting from missile to something else when undocking or switching through the type.
Or create a ship-ai-type that hunts missiles, both solutions do not really feel right.

In T553#19818, @AndyP wrote:

Or create a ship-ai-type that hunts missiles, both solutions do not really feel right.

This would be the simplest of the two probably.

As to why I was using ship instead of turret? For some reason they were set that way after I spawned in the blueprint from SP (set correctly to turret on SP).

which will apparently force the second turret into 'ship' setting

there seemed to be a bit of misunderstanding...

I didn't thoroughly test that part, just left it as is when I saw it happen. All I know is that before it left SP it was set to turret and missile and that is not how it arrived when I blueprinted it in.

Edit: Arrived set one to turret missile other set ship missile

Ok, After some testing it would seem we have the results and they are interesting

The bug the OP was having (or design flaw) is ruled out.

The PD in the middle of the chain do not get ship AI set to them instead an issue like this happens

When not docked to a turret axis you are unable to set the ai to turret (It will revert to ship once you have closed the menu) thus you are not going to be able to set them before docking and that may have been the cause of the OP's orginal issue.

However there are other bugs we found that cause the PD to not fire at all

Chain docking PD turrets make only the last PD docked to the chain be able to turn

The rest are able to fire forwards and only forward of the direction they are pointing

I believe this is an issue with rail turrets and I will be asking if this is intended or not.

you have to take note that in certain turret orientations the axis behaves a little bit weird. The provided blueprint from the op worked fine for me (after manually setting both).
FYI: I declaimed this because i am away on holidays next week.