Let me start by saying that I LOVE the game! However, why am I customizing my character other than for these short cut scenes? Have you had someone else describe your character's appearance to you during a multiplayer match? You do not look like the character that you created. Why is that? Why am I choosing from various options so that nobody can see them? Is this a problem that only my friends and I are having?

nope i have had that problem too. Happened to me for the first time.

I have noticed this as well, it's not a constant problem. I can see my buddies Fallout Tats, then the next game he looked totally different, and we didnt back out to
the menu screen to change character selection.

Ive had that happen to me but it only lasted till i died, after i respawned i was my character, i think its if you join a game in progress you take the body of a bot and the game doesnt change your appearence till you "reset"

I dont remember the last time I saw myself as the character I customised.
Aside from the cutscene in my last freeplay game, of which every character in the cutscene... was me. Same clothing/accessories, the works.
It's a very peculiar situation. I can't imagine it being intentional, but I sincerely hope not.