No, this it is not irrational, that you don't want strangers to touch you. This is common, but also most sensible.
https://en.wikipedia.org/wiki/ProxemicsThe fact that you start this topic, indicates to me that you are suffering from a tension, that you are unable to resolve. That raises the suspicion, that you are hesitating to communicate to your surroundings the terms on which you want to have organised social interaction.
And that maybe you are confronted with commons, that make you uncomfortable. And you don't know how to tell or even demand your needs to/of your surroundings.
This is where I estimate the crux of the matter.
You could be straightforward and communicate you feeling uncomfortably with close speaking distances and being touched directly. In fact from my observation society lacks that people say their real intentions and needs simply open and direct from time to time. Probably because we fear being repelled. The question is: does an alternative tactics exist at all? Maybe yet communicating you feeling uncomfortably non-verbally. I don't see an alternative. Writing a letter. A quite sane person with other customs might react surprised, but why in the world wouldn't he honor your stated needs?