Dragonlance is pretty distinctive among D&D worlds for having such a strong emphasis on the Good/Neutrality/Evil portion of the alignment axis. The gods are broken up into three pantheons because of this.
I don't remember the rule of thumb from AD&D, but I always had the follower's alignment on the good/evil axis match the deity's.
Back in 3.5, the rule of thumb was that a divine servant of a god had to be one alignment step away from the god. So for example, Paladine (LG) could have clerics, paladins, etc. that were LG, NG, or LN. With neutral deities, you could have good and evil characters following a neutral deity, or in the case of Gilean, anybody.
In 5e, they've eliminated alignment restrictions. From page 35 of the Player's Handbook...
So in the context of Dragonlance, how do you think it should work? What are the arguments for and against having a deity's follower's good/neutral/evil alignment match his deity's?As you create a cleric, the most important question to consider is which deity to serve and what principles you want your character to embody. Appendix B includes lists of many of the gods of the universe. Check with your DM to learn which deities are in your campaign. Once you've chosen a deity, consider your cleric's relationship to that god. Did you enter this service willingly? Or did the god choose you, impelling you into service with no regard for your wishes? How do the temple priests of your faith regard you: as a champion or a troublemaker? What are your ultimate goals? Does your deity have a special task for you? Or are you striving to prove yourself worth of a great quest?