Make or Makes for

Solution 1:

To make for is an idiom with several different meanings. In the context of this question, the approximate meaning is 'to produce', 'to represent' or 'to constitute':

Raw earthworms make for grim eating = Raw earthworms represent an unpleasant kind of food

Dobermans make for great guard dogs = Dobermans have the qualities needed to make them great guard dogs

Sowing camomile in your lawn makes for very fragrant picnicking = When you sow camomile in your lawn, the result can be aromatic picnics

People with closed minds makes for terrible leaders is incorrect because the wrong form of 'makes' is used (it doesn't agree in number with 'people'); People with closed minds make for terrible leaders is fine.

In the context of the kind of situation you asked about, as well as in the first two of my examples, 'make' and 'make for' are pretty much equivalent.

'Make for' is slightly more colloquial/conversational. It is also the form that works when you introduce a statement with a verb in the present progressive tense, as in my 'camomile' example.

Both Patrick T. Randolph and J_LV have answered your main point correctly.

Solution 2:

The correct answer is "People with closed minds make" because the subject verb agreement is a plural + plural structure. Does that help?

"People with closed minds" = plural

"Make" = used for plural nouns; i.e., "People make ~."

"Makes" is for third person singular = he/she/it