It sounds rather insecure if it bothers a bride because someone else is in white or off white
On the one hand yes ... on the other hand, the bride probably isn't going to prioritise getting counselling to deal with her insecurities ahead of organising her wedding, so as it's her day, it's just safer & kinder to avoid the off-chance that other guests decide to take offence on the bride's behalf. It's not about anyone thinking a guest could be mistaken for the bride, just about making sure attention isn't diverted into mean comments or backbiting.
Aeons ago, I wore a v simple v white dress to my own wedding. A then-good friend chose to wear a (much nicer!) simple white dress to it. She also happened to be way more attractive than me, & looked stunning - really stand-out-from-the-crowd stunning.
Was I upset? - nah. Friend, looking good, good for her.
However ... a couple of women friends commented (discreetly, not making a socially embarrassing fuss) & looking back at the photos, even putting aside insecure notions about my own attractiveness, my reaction became more... "why would you do that?"
She wasn't trying to "steal the bride's day" or any such hyperbolic nonsense. But she was thoughtless, & a little self-centred. It made me - over a long period of subsquent time - more aware of some of her other behaviours, which I'd been minimising. Double standards, applause-seeking, better at taking help than offering it, double-booking or forgetting firm arrangements to meet ...
Ooops rather long winded self-absorbed ramble there 
- so to get smartly back to @Jadefeather7 ... I hope the 'ramble' illustrates some of the over-thinking & second-guessing some brides, or their guests, might be entering into in this Great British Tradition of Wedding Worrying :)
PS - the red dress is a beauty. Whichever you choose, have fun!