To address the original question, there's no 'must' about it, but people who have been around Highland Dress a long time have developed notions about what looks appropriate.

All the Highland Dress catalogues that I saw when I first started wearing Highland Dress 35 years ago made a clear distinction between "day dress" and "evening dress".

I recently got an old (pre WWII) catalogue and in it fur sporrans are listed with the evening dress jackets, and leather sporrans are listed seperately along with the tweed day jackets.

And these old catatogues have illustrations like this:



These notions persist, as evidenced in this gathering of many of the world's best pipers for a formal event in Glasgow recently:



Here's a pipe band in the 1970's showing the wearing of "day" sporrans with "day dress" (but the PM has an evening sporran)



My seeing thousands of men wearing fur sporrans with evening dress and leather sporrans with day dress over the last 35 years has made that distinction look "right" to my eye.

But...

It's an odd thing... when I thought about it, for some strange reason it looks appropriate for the sporran to be a tad more formal than the rest of the outfit, but not the reverse.

Here are fur sporrans worn with less than formal dress:







and many hundreds of other examples.

About the "hunting sporran", when I got into this in the 70's the traditional "hunting sporran" was brown and worn with "day dress", that is, a tweed day jacket:



But when pipe bands, in the 1980's, began going to the black Argyll jackets, there was a sense that fur evening sporrans were perhaps too formal, but the usual leather pocket with flap day sporrans weren't formal enough.

So somebody at some point got the idea of sticking the cantle from an evening sporran on a hunting sporran, now in black, and these became enormously popular for pipe bands. I've been to competitions where 18 of the 20 bands are wearing this style.

Here it is, the modern Pipe Band sporran:



and being worn by the world's champion pipe band, SFU