Learn Italian: Non devi accettare ogni dogma. - You do not have to accept every dogma.

No, dogma is a masculine noun. It belongs to a special group of Italian words of Greek origin that end in -ma in the singular but are actually masculine. Other common examples from this group include il problema (the problem) and il sistema (the system).

Why does ogni end in "-i" if it's modifying the singular word dogma?

Ogni (every/each) is an invariable adjective, meaning its ending never changes to match the noun it modifies. It is only ever used with singular nouns, so you will always see it as ogni regardless of whether the following noun is masculine or feminine.

How would I say "all dogmas" in the plural?

Because dogma is a masculine noun of Greek origin, its plural ending changes to -i. To say "all dogmas", you would say tutti i dogmi. Remember that ogni is only used with singular nouns, so you must switch to tutti (all) for the plural.

Does non devi mean "you must not" or "you don't have to"?

It can mean both depending on the context! Here, non devi accettare translates best as "you do not have to accept". If you wanted to strongly forbid something ("you must not accept"), the exact same Italian phrase is used, but your tone of voice and the surrounding context would make the meaning clear.