Stomach acid doesnt break down protein, pepsin does.
Antibodies sometimes get broken down by pepsin, sometimes doesnt. Depending on if it has a cleave site. But often even the reduced antibodies still have a protective effect.
For example the IgG antibody has only one cleave site and thus after digestion you are left with what is called half-IgG. Despite being partially broken down this half-IgG still has some effectiveness as an antibody.