Ask them would they preferr u to be bald or have your natural hair? Because, all the methods u are using and the loss of hair can eventually lead to premature baldness. Then ask them, how do they feel about themselve becuase your hair is their hair, basically, they gave it to u. 

I think this is totally ridiculous and ignorant of your parents
(not too mention old-fashioned) but unfortunately this is not the
first time I have heard something along these lines.

When I first met my the women who were to become my
mother-in-law and sister-in-law, my sister-in-law told me that
whenever she wore her hair naturally curly her mother told her
it looked trashy. The problem is, I have naturally curly hair that
is almost identical to the sister's! Imagine how I felt when I
heard this, this woman is looking me over with a fine-tooth
comb so I was nervous enough, but then to find out she detests
curly hair, that was the icing on the cake. What is even worse is
my husband disliked curly hair as well. When we first met the
few times I would wear it naturally curled, he always said it
looked "frizzy or fuzzy." Now he is so used to seeing me go au
natural that I think it has grown on him, although I know he
would still probably prefer me to have stick straight  flatironed
hair (every single one of his exes had the same hair). Some
people just have a thing against curls, I personally don't see
what the big fuss is about.