What you are asking runs counter to Lovecraft's Mythos.
Most, if not all cultist are insane and incapable of such a degree of planning as is shown in The Call Of Cthulhu.
There are some powerful sorcerers in the world with a strong enough will to accept the cosmic horrors as their own. However, they do not play well together nor do they really care about what the world thinks. However, most if not all magic has to do with contacting and summoning other worldly creatures. There are few illusions, invisibility, mind control, or other spells and most of those are RPG inventions not Lovecraft's. Most other forms of magic are done by over worldly creatures and are mostly science far too advanced for mere humans to understand.
In The Shadow Over Innsmouth, a whole town serves as a hiding place for a cult of Father Dagon and Mother Hydra. Most of the inhabitant are a mix of Deep Ones and humans but they still get found out. However, that is more to do with it being a story.
The latter, I feel, is your best bet. If the locals are all part of the cult, then anyone coming in can be watched, warned, and steered away from the cave.
Nothing like getting arrested for drug possession, or maybe child porn. After all, what did that 12 year old girl doing tied in the interloper's room? Especially since she went missing after many witnesses saw her talking to the interloper. Besides, accidents happen. It's a tragedy. Better not hike there.
If someone manages to get there, driving them insane (read: forcing them to join the cult) seems like a good plan. If you're ranting about rats living under your skin, no one will pay any attention to what you say. Any summoning spell has a great potential to drive the melding fool insane. And if it fails, the creature can always eat them. However, note that none of the summon spells ever include a (working) controlling part. The creature is free to do as it pleases, including eat the summoner.
Finally, explosives make for a great eraser of evidence. Several kilos of C4 will make sure the cave is never seen by anyone. Sure, the cult loses it but is that worst than being on the five o'clock news?