The Church has about 55,000 missionaries worldwide, all of whom follow the same basic dress code and go about in pairs, basically recruiting people to join the organization. For men, white shirt and ‘conservative’ tie, suitjacket if it’s cold. Clean-shaven. No chewing gum in public. Short hair. And so forth.

I have to wonder if this is really optimal. I've often heard people poke fun at LDS missionaries for exactly this image. Possibly it exudes respectability on a level that people who aren't receptive don't want to acknowledge, but has the church ever experimented with this?

It's hard to compare the relative growth rates of religions because so many do not keep good statistics, and besides which, many databases do not keep statistics for the LDS church separate from those of mainstream Christianity, but the Baha'i faith seems to have had comparable if slightly lesser growth, and far more international success.

Many religions throughout history have achieved explosive growth rates, but none so far as I know have done significant experimentation to optimize their methodology, and a lot of religious conversion tactics rely on what we consider here to be Dark Arts, which are not nearly as conducive to encouraging people to become rationalists.