Is "All" the subject in this sentence or is "who" the subject?
If all is the subject then believe would be the correct verb agreement. If who is the subject then believes would be the correct verb agreement.
So which is the subject please?
All who believe is not a sentence; it's a noun phrase.
Taking a sentence starting with all who believe we get
All who believe are believers.
The correct verb form is believe.
Who is not bound to third person singular verb form.
The people who believe are believers.
Who takes the verb form of the subject the people.
Neighbors who insist on believing are believers.
Who insist on believing is the relative clause. But who is plural in this case because its antecedent is the plural subject neighbors.
The same concept goes for
Who am I?
Who is not third person singular. Its verb agrees with the subject it's standing for.
I who believe am a believer.
Who stands for I, which takes am.
As another example showing who is not always third person singular is
You people who are here believe.
Who takes the verb that agrees with you people (second person plural).
Also, second person singular:
Who are you?
You, who are my best friend, are a believer.
Finally, you can also say
All that believe are believers.
That substitution should be a hint that the relative pronoun can be either either singular or plural.