You can use (almost) any weapon against shields or hull. It's just that thermal weapons are more efficient against shields, and kinetic weapons are more efficient against hulls. On the other hand, if you have equipped one of each, the combination of both will still be more effective than just using one - against either shields or hull.
If it's uo again, you can play around with different weapon configurations in
Coriolis (offense or defense tab, plug together your opponent and check how fastr you can kill them and vice versa).
Coming to the exceptions:
- explosive weapons (missiles) are nearly useless against shields, but extremely effeective against exposed modules (like guns - or thrusters) once the shields are down
- there's one powerplay weapon, the Cytoscrambler, which is extremely good against shields but doesn't do any (or nearly) damage against hulls
Single type loadouts: sure - with exceptions.
I have a loadout for my Mamba with mainly efficient thermal vent beams, plus two small gimballed multicannon (or fixed Enforcers, i.e. powerplay MC). The MCs are there to deal special effects, in that case Corrosive Shell, which weakens the hull by IIRC 30%. The lasers work a charm also against hulls, and since it's hitscan, it's a safe as it gets for combat zones.
In the other corner is my general purpose Krait Mk.II - fully kinetic. 3 (large) Pacifiers (powerplay fragment cannon) on the top, two medium gimballed MC next to the cockpit. Again, one of the MCs equipped with corrosive, the other with incendiary. I hate to wast the corrosive effect on the Pacifiers, and the Krait isn't quite nimble enough (when I'm flying it) to hit small fighters with fixed weapons. And even though the Pacifiers are strictly kinetic, NPC Anacondas usually (2 out of 3) don't manage to go through a SCB cycle before they're down. Just don't take frags into a CZ.