This is not a completely new idea. There's a thought that there are
four kinds of cyclists. The one's bragging at their utility cycling or the LCF-ness are probably the "Strong and fearless" types. It's been pointed out that the most effective advocacy would actually target the larger "Interested but concerned" group. '
Instead of being an LCF-Now!!! militant, suggest that those who are interested in riding more merely do so. Run an errand on a bike. Do some cycling activities. Work up to a commute.
Instead of going off on how everyone cycling will change the world, heal the environment, etc., focus more on the practical aspects -- saves money, healthy -- and don't forget to mention that riding is fun.
Instead of scoffing at what you may think is not legitimate concerns, talk people through your decision-making so they know the reasoning behind why you don't think what they are concerned about is such a big deal.
Ultimately, leading by example is the best way to encourage anything. Like many other things, success will be if LCF becomes something which is attractive, rather than something it is necessary to promote.