I must admit, that despite being nearly 60, I have never come across hordes of "non-religious" people giving up things for lent, or not eating meat today.
Why would somebody do that if they weren't religious ?
I was brought up as a Catholic in the 1950's and 1960's, and went to a Catholic school, where I was taught by a motley crew of nuns and brothers.
Giving something up for Lent wasn't an option back then...it was compulsory, especially if you were 10 years old. The nuns used to tell us that we should make the sacrifice and give up something, although the reason and rational of so doing was never fully explained. It was one of "Gods mysteries" along with millions of babies dying in African famines.
I suggested one year that I was going to give up cabbage, and sprouts for Lent. The nuns were horrified, and asked me to explain. So I told them my Mum always told my brothers and I that cabbage and sprouts were very "good for you", thus making their absence from our diet a really good sacrifice.
I thought my reasoning in this matter was unimpeachable but the logic seemed lost on the nuns altogether. Much use of the cane ensued.