In adventure mode, you can interact with light blocks

Can confirm.

I can confirm this behavior in 1.18.1.

Here's a code analysis along with a potential fix regarding this issue.

Code Analysis:

The following is based on a decompiled version of Minecraft 1.18.1 using MCP-Reborn.

net.minecraft.world.level.block.LightBlock.java

public class LightBlock extends Block implements SimpleWaterloggedBlock {
   ...
   public InteractionResult use(BlockState $bs, Level $l, BlockPos $bp, Player $p, InteractionHand $ih, BlockHitResult $bhr) {
      if (!$l.isClientSide) {
         $l.setBlock($bp, $bs.cycle(LEVEL), 2);
         return InteractionResult.SUCCESS;
      } else {
         return InteractionResult.CONSUME;
      }
   }
   ...

If we look at the above class, we can see that no checks are carried out to see what abilities the player possesses when interacting with a light block. The only check that is in place is to see whether or not the action wasn't client-side. This is evident through the following line of code:

if (!$l.isClientSide)

Potential Fix:

Simply adding a line of code that checks what abilities the player possesses before interacting with a light block, should resolve this problem. The following line of code could be used in order to fix this:

!$p.getAbilities().mayBuild

Can confirm in 1.18.2 and 22w12a.

Fixed in 1.19.3 pre-release 3, as modifying light blocks requires creative mode and level two operator (LightBlock#onUse method in Yarn mappings)