Avoiding eye contact altogether in public

My mother advised me it's best to avoid eye contact with people completely in public.

What are your thoughts on that?

I felt it was rude to do that but tried it while we were out in supermarkets shopping earlier on, and although it felt odd and somewhat ignorant, and also I missed seeing who was near me - in case I recognised someone or there was someone interesting to look at - I think I felt more calm and less overloaded in the way that can lead up to an Autistic meltdown.