vignette says "If within a row, all samples have zero counts, the baseMean column will be zero, and the log2 fold change estimates, p value and adjusted p value will all be set to NA."

This seems to mean that the zero-sum rows can be kept in the input data.

But whether I exclude the rows with zero-sum or not, the results are different. So what is the correct way to analyze the data?

You can exclude to make the dataset smaller size.