You are correct that rental of personal property or provision of services along with the rental of real estate for general income, and not for related programmatic reasons, can cause rental income that is otherwise exempt from UBIT to become subject to UBIT.  The same occurs with unrelated rental of debt-financed property.  (See Ready Reference Page:  “Charities Often Worry About UBIT”)

But if you are renting it to fulfill your charitable purpose, it will not be subject to UBIT.  A 501(c)(3) low-income housing developer receives program service revenue from the rental of its apartments to low income families.  A university receives program service revenue from rental of its dormitory rooms to students.  Both of those developments are usually debt-financed, and the landlord may be providing additional services along with the rental.

Notice that the related rental income is recorded on the Form 990 tax information return as program service revenue on Line 2, and not as rent on line 6 on the income statement in Part VIII on page 9.  We once reviewed the 990 of a community center in a low income community that rented out space in its building to social service providers and government agencies specifically brought together to create a one-stop help center.  The 990 listed all of the rental income as rent on line 6 rather than program service revenue on line 2.  It looked like the organization had no charitable program at all, which could have raised a red flag with the IRS or confused potential donors doing due diligence before considering a contribution. 

Listing the income as program service revenue can also help the public support calculation on Schedule A.  It will be excluded from investment income in the denominator of the fraction if you are qualifying under Section 509(a)(1) and will go to the numerator of the fraction rather than to the denominator only if you are claiming public support under Section 509(a)(2).  (See Ready Reference Page:  “Calculating Public Support”)