I think that experience and improvement on bowing helps and enables one to play these strings, steel and E strings. You don't hear it with the real experienced violinists. 

Pay attention to your bowing and try to make note of it when you hear these unwanted sounds and practice and see how to do it without that sound. Like practicing intonation on the fingerboard, do it over and over. The same thing with bowing. Practice bowing the E string open, first finger, etc. Practice going from the A string to the E string. Other notes and strings to the E string. Not bang bang bang. Listen and pay attention and spend time on one exercise until you get it. Then add to it. 

Sounds simplistic when I type it, but it isn't. Professional and experienced violinists spent many many years honing that skill. Some strings are better, but it depends on the student violinist. I bought the Kaplan non-whistling E over a year ago because people swore by it. I didn't hear a whistle at first, then I did. I think it was because I was actually paying attention to see if I could hear it when I first got it. 

I love my set of Evah gold label strings I just put on my violin, it may help someone's E string issue, but it has to do with bowing, the fingering when not playing open E. Maybe getting a string that is recommended by someone as not being a whistling E will work, if for no other reason than you are paying attention to the bowing (angle, pressure, etc) and fingering and going from string to string. If that is the case, it is worth it.

Love having you here.

I love the Fiddlerman strings on my Fiddlerman Concert Deluxe.