Can you take the Apache trail loop 88-188- 60 with a rental car?
Most companies do not allow "off road travel" which means dirt roads. Apache (88) is a dirt road so, no.
How's New Ulm? Got a good friend that lives there. I lived in Madelia for a few years, heard they had a bad fire downtown.
theoretically, yes, but the whole 20+ miles after Tortilla Flat is unpavd.You don;t ned 4x4 or high clearancem, but it's a very rough ride with lots of heavy washboarding. You're not 'off-roading', it's an official road, just unpaved ... so, yes,you can, but if you really should is a different question.
...and theoretically no. Many rental companies do not allow driving on unpaved roads. This is from Enterprise's terms and conditions:
"4. Limits on Use and Termination of Right to Use.
a. Renter agrees to the following limits on use:
(10) Vehicle shall not be driven on an unpaved road or off-road."
If you really want to do it, contact the rental agency and get a copy of their terms and conditions (specifically the one that you will be signing when you rent the car). But as Esty666 said, "if you really should is a different question."