Baptism is a public act.
It may very well be a public act, but that doesn’t mean not taking into account circumstances. His identity as a christian should have been kept secret. What do you think would have happened to all Christians in the roman empire if they would’ve gone jumping about the streets declaring themselves christian? As you recall, in the first centuries Christians would gather in secret to celebrate Mass. So, I highly doubt this to be the correct course of action.
obviously he should have joined the Catholic church. the only time they publicize baptisms is babies and Easter Vigil.