The danger in ignoring nofollow sites
If you choose to ignore the websites that allow you to leave a link, but it is nofollow you will probably end up looking bad in the eyes of major search engines like Google. It is assumed that if you are getting a lot of backlinks, other people must find what you have to say of value. So whether or not you get at least a few of them is not going to always be in your control.
The websites that do not follow backlinks might decide to use some of your content and include the link. Google is well aware of this, and it is something that would occur whether you wanted it to or not. If you have nothing but dofollow backlinks, this looks very deliberate and fishy.