At the end of the day, you need happy customers so that you get good referrals, and you need to weigh your options accordingly. When you own a business you need to be sure you're making as many customers as happy as possible, even if it goes against your aesthetic. user concord made an excellent point in asking the customer to sign a waiver that you will not be held responsible for a stained dress.
If you want to convince the bride not to use them, tell her a story about how a shop you worked at before went out of business because the bride wanted purple tainted flowers, and while she was walking down the aisle the paint started dripping down her dress and made a huge mess, and the colors separated and there was a large red splotch really close to her groin, surrounded by a blue-black stain making it look like she was going through some really painful moments, and the wedding was cancelled halfway through and the groom's family sued the florist because all the money he put into the event was wasted because his former bride was now in a mental institution... or something like that. Make it lively and detailed, and make her laugh and she'll get your point. If she really wants it, I think you should do it and make her happy. She'll only have good things to say about you to all her friends, family and coworkers.
Then if all else fails I would do it, but deliver in an unmarked vehicle and not use any branded packaging. As long as you do a good job with the design what does it really matter if it's not your taste? The customer pays you to get what they want, not what you want IMO. I don't carry dyed flowers either and I detest them, but if someone really wants them I will special order them because that's what I feel makes good customer service. When I am on the fence about something like this, I try to look at it from a different perspective. What if you wanted a blue dress but the dress shop said no, blue is ugly we won't carry it. You know it's available, but the shop refuses to order the dress in blue. Would you change to pink or would you go to a different dress shop? That said, maybe you really don't care if she goes to another florist to get blue dyed roses and in that case, just tell her you've built your reputation on a natural style and you can't use dyed flowers. You might even refer her to a florist who will help her which makes you the helpful florist instead of the snooty florist. Good luck with whatever you decide and keep us posted. One thing I do know is we all work too hard to do something that we don't feel right about, but we all have different opinions about how to run our shops and I don't think there's a right or wrong as long as you are profitable.
