This is easily resolved for the devs by altering their Edition pre-req from:

<InterpreterPrerequisite Flags="Edition">Path(Context, @ShipRoleSupport) or Path(Context, @ShipRoleCarrier)</InterpreterPrerequisite>

to

<InterpreterPrerequisite Flags="Edition">Path(Context, @'ClassShip,ShipRoleCarrier') or Path(Context, @'ClassShip,ShipRoleMediumSupport')</InterpreterPrerequisite>

Aitarus' fix works, but I had to figure out where this was exactly [I am VERY bugged by these game "bugs"].

How: edit file: ModuleDefinitions[Support].xml

Starting at around line 966 you'll see this and this is where I added the lines [you'll just need to copy/paste InterpreterPrerequisite line twice]:

    <!-- ********************************** -->

    <!-- *****      F/B MODULES        **** -->

    <!-- ********************************** -->

    <SupportModule Name="ModuleSupportSquadronOffenseEnhancer1Strategic4" Family="SquadronOffenseEnhancerStrategic4" Level="1">

        <Cost ResourceName="SystemProduction">70</Cost>

        <Cost ResourceName="Strategic4" Instant="true">2</Cost>

        <TechnologyPrerequisite Flags="Edition">TechnologySupportModule5</TechnologyPrerequisite>

        <InterpreterPrerequisite Flags="Edition">Path(Context, @'ClassShip,ShipRoleCarrier') or Path(Context, @'ClassShip,ShipRoleMediumSupport')</InterpreterPrerequisite>

        <SimulationDescriptorReference Name="ClassModuleSupport"/>

        <SimulationDescriptorReference Name="ModuleTypeStrategic" />

        <SimulationDescriptorReference Name="ModuleSupportSquadronOffenseEnhancer"/>

        <SimulationDescriptorReference Name="ModuleSupportSquadronOffenseEnhancer1Strategic4"/>

    </SupportModule>

    <SupportModule Name="ModuleSupportSquadronDefenseEnhancer1Strategic3" Family="SquadronDefenseEnhancerStrategic3" Level="1">

        <Cost ResourceName="SystemProduction">70</Cost>

        <Cost ResourceName="Strategic3" Instant="true">2</Cost>

        <TechnologyPrerequisite Flags="Edition">TechnologySupportModule1</TechnologyPrerequisite>

        <InterpreterPrerequisite Flags="Edition">Path(Context, @'ClassShip,ShipRoleCarrier') or Path(Context, @'ClassShip,ShipRoleMediumSupport')</InterpreterPrerequisite>

        <SimulationDescriptorReference Name="ClassModuleSupport"/>

        <SimulationDescriptorReference Name="ModuleTypeStrategic" />

        <SimulationDescriptorReference Name="ModuleSupportSquadronDefenseEnhancer"/>

        <SimulationDescriptorReference Name="ModuleSupportSquadronDefenseEnhancer1Strategic3"/>

    </SupportModule>

I'll report back if something goes wrong, but so far so good.  It would be great if we had a master list of minor fixes that aren't fixed so we can do it ourselves :)