I've sort of have this, although it's mainly pauresis that is the problem. As I've dealt with my pauresis this becomes less of a problem.
Basically, I can poop if really needed in most situations but just get critically embarrassed if I fart or make much noise, which sort of 'clamps' up my insides (I'm sure you all know the feeling). I guess because I grew up in a big house and never (to my memory) heard anyone else ever go to the toilet, so I just thought myself as weird if I did make a noise, which is fairly frequently - I've never been diagnosed with any sort of intestinal issue but I don't always have the smoothest of poops (although I find the squat position far superior and much better quality poops).
So... out of interest, how much noise is normal? I know consciously no-body cares about what I do in the toilet but some reassurance would subconsciously help.
I think I need to practise, too. Rather than avoid the situation I deliberately went to a public bathroom today and have been making myself use the loos at work. It is usually okay but it can feel like I didn't fully relax. So... I think what I need to do is really focus on relaxation when on the loo! Remind myself no-one cares whatever noise I make and even if I do, just embrace it, it's all natural and we all do it.