[RPG] What creature types are Gods

There is Karsakim. He is the leader of a military force dedicated to eradicating religion in Rahadoum.

Apart from that pathfinder has some abilities that require you to not follow a god.

One example is the feat godless healing

"Godless Healing

You have mastered a specialized and complex technique to ignore pain by focusing your belief on the self rather than relying on faith.

Prerequisites: Cannot have a patron deity.

Benefit: Once per day when you have half your total hit points or fewer, you may heal yourself of an amount of damage equal to 1d8 plus your total Hit Dice as a move action. This is a supernatural ability.

Special: You can take this feat more than once. Each time you do, you may heal yourself one additional time per day."

Beside the above mentioned Rahadoum in Garund there are Touvette in the River Kingdoms and Bachuan in Tian Xia that discourage or forbid religious practice.

The number of worshippers is not necessarily countable: the polytheism of the Realms is such that people venerate many members of the pantheon. You might have a patron deity, but you might still pray to another on particular occasions. Quoting from the 2e sourcebook Faiths & Avatars (F&A):

What matters to a particular Realms power is not that a follower worships someone else - most everyone in the Realms worships several someone elses - but rather which other powers are venerated and which are appeased, and how serious a person's offerings and worship are to other deities.

Hence an inquisition like the one you describe in your question does not sound very likely on Faerûn.

Moreover, many powers are allied. For example, Mystra has Velsharoon, Azuth and Savras serving her. Deneir, Gond, Lliira and Milil serve Oghma, etc. Hence an alliance of greater gods against the lesser ones again seems unlikely. Actually, F&A also provides a rough answer to the following question: Given that the power of the deities come from their followers, why do the greater gods let the lesser ones live? (1) Greater powers protect them against other greater powers; (2) Weaker deities pay some amount of divine power to the greater deities, willingly or through extortion. So again, it is unlikely that the greater deities would gang up against the lesser ones.

But if we leave aside the motivation for your question, and focus on the power of each deity from a pure mechanical point of view (as power correlates strongly with the collective amount of worship received), there is one source that provides the information you are asking for: 3e sourcebook Faiths & Pantheons (F&P). Beyond the demi-lesser-intermediate-greater categorisation that appears in most editions of D&D, this book also defines a "divine rank, which is similar to a character's level". While 4e has changed a lot of things about the FR pantheon, 5e appears to be a very strong return to the flavor of 3e FR, with dead or missing deities returning to pretty much to how they were in 3e (or even 2e). So the divine rank from F&P should give you an idea.

According to F&P, a divine rank of 21+ is only for an overdeity (like Ao), and such deities are not interested in mortal affairs. So the "big" guys are the greater powers, with divine ranks in the range 16–20. Quoting F&P, greater deities "have millions of mortal worshipers", whereas the intermediate ones "have hundreds of thousands". (I assume this is again not an ordinary count, but a collective effective measure.) I list below the divine ranks of greater deities from F&P:

Rank 20: —
Rank 19: Chauntea
Rank 18: Mystra, Shar, Silvanus, Tyr
Rank 17: Bane, Cyric, Kossuth, Lathander, Tempus
Rank 16: Kelemvor, Oghma, Sune, Talos

Note: The divine rank for a few greater deities is not listed: Akadi, Grumbar, Istishia, and Ubtao. The first three of these can be considered similar to (or weaker than) Kossuth, as they are all elemental powers. Ubtao's faith is strong only around Chult.

Reading through the deity descriptions in Sword Coast Adventurer's Guide, the power level differences appear to be less pronounced compared to earlier editions. But one can perceive similar power structures amongst the deities. For example, Deneir and Milil are said to be "sometimes thought of as being in service to Oghma". So you might perhaps want to slightly modify the list above, but overall I hope the list provides enough insight to finding the answer to your question.