IDK about all products and garments but some items I keep the tag on because the item is brand name. For example: I'm not about to cut the tags out of my Agent Provocateur lingerie or my Burberry jeans... This reminds me to care for the items better while washing/drying and storing. Additionally if in a bind I could resell the items on ebay or somewhere. People are always hunting down brand name items for a deal.  

But for the 25$ bikini or 50$ lingerie set, IDK why someone would leave the tags on unless they weren't visible.

I always figured the tags are left on to help figure out the front from the back or which hole to...

...put your leg through. I get so confused sometimes when I try on women's lingerie that it looks like my dick got caught all snarled up in a fight with the line from my fishing lure!  

cutting the tag off can leave a hole or worse yet if you cant cut deep enough into the seam you are left with a scratchy piece of tag which is uncomfortable.
Having said that - I DO cut my tags off if they are obviously visible.

Then there's the whole weird phenomena of "fresh"
I had never seen "fresh" until i came to America.  I was amazed at all the people walking about with full tags / carboard labels on plastic strings still on their sneakers, stickers on their hats etc.. they look like they had just walked right out of the store with a shoplifted item.
I asked my friend what it was about and he told me its called "fresh" - a concept that started in the ghettos and its supposed to show off that you purchased the item and didnt get a handme down/thrift store piece.  Has spread thru culture via the music and video media.

I think its absolutely ridiculous

What does it matter anyway, The bathing suit is see through,lol. Ild say go commando! The tag is covering up some pubes!