I am confused by two IRS rules on rentals which seem to contradict one
another.

Consider a person who rents a couple of rooms in his house out to tenants.
He deducts a pro-rated portion of various house expenses (such as utilities,
property tax, mortgage interest, depreciation, etc.) on Schedule E based on
the square footage he rents out compared to the total square footage of the
house. This person is not a real estate pro, and meets all the requirements
for actively managing the rental and for it being passive income, etc. The
rental results in a small tax loss each year of a couple of thousand
dollars. The question is can he report this loss (i.e., negative income) on
his tax return each year to offset his regular income from employment, etc.

On one hand, I see a rule that says you have to show a profit in 3 out of 5
years to establish that you are renting for profit. On the other hand, I see
a rule that says you can deduct up to $25,000 in rental losses each year
assuming you meet all the rules for passive, active, etc. Don't these rules
contradict one another?

Here are the rules from Pub 527 that I'm talking about:

"If you do not rent your property to make a profit, you can deduct your
rental expenses only up to the amount of your rental income. You cannot
deduct a loss or carry forward to the next year any rental expenses that are
more than your rental income for the year." It further states "If your
rental income is more than your rental expenses for at least 3 years out of
a period of 5 consecutive years, you are presumed to be renting your
property to make a profit."

That seems pretty clear cut.

But in another section of the same manual it says: "If you or your spouse
actively participated in a passive rental real estate activity, you may be
able to deduct up to $25,000 of loss from the activity from your nonpassive
income. This special allowance is an exception to the general rule
disallowing losses in excess of income from passive activities. Similarly,
you may be able to offset credits from the activity against the tax on up to
$25,000 of nonpassive income after taking into account any losses allowed
under this exception."

No mention here of having to show a profit 3 out of 5 years.

How do we reconcile these two seemingly contradictory instructions?

I should note one other thing. In this case, the owner actually does make a real profit on the rental each year, but it shows up on the return as a loss (i.e., negative rental income) because included in his rental expenses on Schedule E is a pro-rated portion of his mortgage and property tax expense reflecting the portion of the house he rents out (the remaining part of his tax and mortgage interest is included on Schedule A). In reality, these expenses would be incurred and deducted in full on schedule A whether or not he does the rental. If you exclude them from Schedule E, he actually shows a net positive rental income. But I don't know if the IRS would look it that way in assessing whether or not he has negative rental income.