What does “snug as a nun’s wimple or loose as a suggestion mean?

Solution 1:

In your example sentence, the right clip should be as follows:

Hijab that can be worn snug as a nun’s wimple / or loose as a suggestion...

The bold parts are being contrasted. Loose as a suggestion is not an idiom or popular set of words.

Suggestion means:

A slight indication of something

Snug means:

Very tight or close-fitting

The adjective loose is an antonym of snug.

So your example could be rephrased to:

Hijab (which was not allowed to be worn loosely in the past) can be worn (either) very tightly like a nun’s wimple or loosely as a suggestion of change (from the past in terms of sexuality, attitude, and way of thinking) of a woman...

Now it is allowed for Iranian women to wear Hijab more loosely than before to express their attitude or way of thinking towards sexuality.

[Oxford Online Dictionary]

Solution 2:

No, it is not a popular set of words. Loose as a suggestion is a simile apparently devised by the author of that article (judging by the fact that all Google hits for that collocation point right to it).

Apparently the author perceives (many) suggestions as inherently loose (reading vague perhaps), which grounds the simile here. Another reading, bordering on guesswork of course, may be loose as a suggestion of a Hijab, meaning that the wearer can express herself by adjusting her Hijab loosely rather than tightly.