German point of view here. 

> what is the justification used to separate certain beliefs (flat earth) from others (religions), and why is it legal to discriminate against one but not the other?

This is *not* the case in Germany. In
[basic law](https://www.gesetze-im-internet.de/englisch_gg/englisch_gg.html) (constitution) religion typically appears as "religios or philosophical creed" or in other combinations that avoid the distinction OP is asking for: 

> Art. 3 (3) No person shall be favoured or disfavoured because of sex, parentage, race, language, homeland and origin, faith, or religious or political opinions. No person shall be disfavoured because of disability.


Note that this anti-discrimination list for legislation also covers a number of non-religious points that are choice rather than in-born, e.g. language, homeland and religious as well as political opintions - also sex and disability are protected regardless of their "origin" (trans-sexuality, self-inflicted disability, accident/illness or congenital disability don't matter from a anti-discrimination pov). 


> Art. 4 (1) Freedom of faith and of conscience, and freedom to profess a religious or philosophical creed, shall be inviolable.

> Art. 33 (3) Neither the enjoyment of civil and political rights, nor eligibility for public office, nor rights acquired in the public service shall be dependent upon religious affiliation. No one may be disadvantaged by reason of adherence or non-adherence to a particular religious denomination or philosophical creed.

So as long as your flat-earther is a faithful flat-earther, they're covered. Just as Christians, Jews, Atheists, Agnostics, and you-name-it.

In fact, what is colloquially called "church" in legal terms is referred to as   "Religions- und Weltanschauungsgemeinschaften" where Weltanschauung is any kind of belief (Gemeinschaft = community). We do have e.g. humanitarian communities that have a legal status like, say, the Catholic Church. 
 

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Note that the basic law defines rights of people against the Federal Republic, so for private person doing service the rules may be relaxed. The "Public space" and labor law are also covered by anti-discrimination laws: if you run a shop that is open to the public and that will naturally serve many customers, you cannot arbitrarily deny services. You can throw out the "asshole" of the question in case they are an asshole because they misbehaved in your shop, though. If your service is to rent out a single room in the 2nd floor of your house, you are not forced to install an elevator so as to not discriminate against certain groups of disabled. And you are allowed to select your renter by percercieved likelihood of paying the rent. 

Some more limits to anti-discrimination: 

- a blind person does not have the right to be employed as bus-driver
- a Lutheran Church is allowed to require their employees to be Lutheran as well,
- a political party can refuse membership to members of another political party. 
- the police or a security service may refuse to employ an ex-convict as police officer/security guard. (But I wouldn't be sure that this would be true also for a janitor or mechanic job)