I took a closer look at Dragonlance Adventures, and it doesn't say you can't be a Paladin. What it says is:It's complicated. When Dragonlance was originally published there was no prohibition on paladins, but no official pregen paladins. Then, when Dragonlance Adventures was published (still 1st edition) it re-tooled the paladin class into a Solamnic Knight class, as well as re-tooling the Magic User class into a Wizard of high sorcery class. So at that time, the setting didn't have Paladins (or Magic Users). It had characters who walked like paladins and quacked like paladins, but were called Solamnic Knights.
So you have to worship a local god, and you may join the Knights of Solamnia, but you do not have to. Otherwise, you are a knight operating under the direction of another organization.