Is it acceptable to mountain bike on narrow hiking trails?(Minnesota)
It depends on the local laws, both regional and countrywide. It's not really a question of acceptable or not.

e.g In England trails can be strictly footpath which means no bikes. Bridleways, Byeways and Byeways Open to All Traffic (BOATs) can be ridden by bike with pedestrian priority.

Find out the local laws for your region. 

If you do find that all your local trails are fair game it's still up to you to ride in control and with courtesy. Any person &amp; bike collision will be your fault.