Impact of tax class on creditworthiness

Every bank employee who checks loans must know that the tax class has no influence on the amount of the annual net income.

The bank employee does not. But for a standard financing, NOBODY bothers to calculate a monthly net income from the tax return. Advertising expenses, possibly expenses for double housekeeping, etc., also play a role here.
Besides, the decision is mainly made by a machine. And there, only "monthly net income from the payslip" or other income such as bonus etc. are entered.

However, if the credit decision fails because of the tax class, the whole idea of building a house is nonsense anyway.

The only right decision in this case is to claim additional parental allowance by switching the tax class and switching back after the birth. We did it that way as well and there were no problems with the credit decision. If one bank refuses, there are still 100 others. Just request offers through a financial intermediary. If the other creditworthiness including the equity share is correct, the temporary tax class switch is absolutely negligible.