their recollection may be at fault, they may have misunderstood what the priest said, or they may have assumed something he did not actually say, or heard misinformation from parish staff. It is more likely that the priest gave them extra time to find a godparent, or for another reason suggested a delay in the baptism, not that he denied it. Yes there have been parishes that have a pledge or tithing policy and used to ask for proof of income, that is now discouraged, but even then it was never allowed as a reason to deny sacraments.
What is now and was then policy is that the pastor of your territorial parish has jurisdiction over all Catholics within his parish boundaries, for purposes of all sacraments especially baptism. They may have as new parents not have an established parish yet, and the priest asked for some evidence that they were active practicing Catholics and would raise you that way, and they interpreted him as being much stricter. When we married, moved to another city and tried to register we had to skip 3 ethnic parishes closer to him and find one that would accept us “generic” Catholics, and that priest said flat out, 5% to the parish and 5% to other Catholic charities or organizations, of our take home pay. He did not ask for proof but he stated it as if it is a general rule. He “dispensed” the 2nd 5% since DH was attending a Catholic college and paying tuition there. We have held to that pattern throughout our marriage, one of the best things we have ever done.
anyhow welcome home there is a special grace in making the journey this way through RCIA. That was then, this is now, and we live in now. View your journey that way and savor every step, as all is grace. Surprising things may happen as this grace extends to the entire family.