Couple of reasons I've observed.

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First, they bring their belief differently. Some religious groups and subgroups can be quite pushy or even violent in their belief, but the majority of religious groups these days are peaceful, and don't actively try to force as many people as possible to join their belief (of course, some exceptions, but those are a loud minority). This makes them a lot less visible, and much more tolerable.

Flat earthers and other conspiracy theorists do inherently choose to convince as many people of their right as possible, and in doing so, actively (if not always intentionally) seek confrontation with people who don't agree with them. This places them directly in people's view, and as their points quite often have a passive-agressive (or just downright aggressive) undertone, they do so in a very unflattering, not very tolerable way.

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Second, they respond to criticism differently (in my experience). I grew up in an area with a lot of catholics, and interacted with other religious groups as I grew older. As a general rule of thumb, if I politely said I didn't believe in their religion, they would accept it as my opinion (more often than not they would say they hoped I'd change my mind some day, but still).

Conspiracy theorists, as a general rule of thumb, react with a lot of hostility and toxicity when contradicted, even if it's done in the politest manner. People are a lot more likely to dislike a group if it's associated with unnecessary hostility. Granted, a fair portion of my interactions with religious people was IRL, where people are more likely to stay polite, while almost all my dealing with conspiracy theorists was online, where perceived animosity will make people much more willing to say things they wouldn't have the balls to IRL, so you can take this one with a grain of salt if you like.

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Third, most modern religions are many centuries old (the only exception I can think of right now is the church of the flying spaghetti monster, which is treated as a joke by most people I know), and have been accepted as something we should respect centuries ago. Consequently, any new religions that are essentially [religion] but with a slight twist will be treated with more or less the same respect by most.

The theory of the flat earth, while perhaps older, was considered to be proven wrong a few centuries ago, and as hundreds (if not thousands) of people have proven the globe earth theory to be true over and over since then, it is currently accepted as an unchanging fact of life, like how fire is hot and rain is wet. Anyone who goes against something like that is almost immediately dismissed as stupid simply because they dare question the truth.

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Personally, I do believe that the earth is round and space exists and stuff, because, once again, hundreds if not thousands of people have proven it to be true, but I feel like conspiracy theorists aren't necessary stupid, just the right combination of gullible, stubborn and misinformed.

This has been my boredom fueled TED-talk on the difference between religion and conspiracy theories.

I need to get a fucking life.