While it is true that "speak up" is used to encourage someone to speak more audibly, both "speak up/out" are used to mean expressing one's views, especially in a public setting. There are usually some things which we perceive as unjust and would like to make them publicly known when we "speak up/out".
Could you speak up, please? (raise your voice)
We must speak up (publicly voice our support) for these indigent communities.
Someone has to speak up for the marginalised.
If we do not speak out (publicly highlight some issues such as unfairness) against the system, the ones to suffer will be our future generations.