There is good netting that doesn't tangle birds or the tree. I haven't used anything from American netting but it is often recommended: https://www.americannettings.com/product/bird-netting/

I have used black woven 30% polypropylene shade cloth for 40 yrs. That's the same pieces for 40 yrs and covering 3 of my trees as we speak. It's a bit heavy but hasn't hurt my trees when left on about one month. This is small pieces over small trees:

I have 30x30ft pieces for bigger trees and here as hail netting over melons:

There are many suppliers of woven and knit shade cloth. I'd recommend the edging and grommets as seen on mine.

http://www.shadeclothstore.com/products/wovenshadecloth30__wovenshadecloth.html

We use reflective tape and its not and issue.

As long the netting is not the thin stuff...and the hole size should be small.

Try to keep the netting taught. If it is loose it is easier for birds to get stuck in it.

No matter how hard you try, there will be the occasional bird that will get caught.

Oh I will never get over the horror of finding a flock of birds caught in my netting, and struggling to get out! My son finally had to hold each bird in his fist and cut away the netting, especially as some birds got their heads stuck in it! He was in middle school then, and the only one amongst us who had the nerves to do it with all the flutterings around him! I pick my fruit underripe now and ripen on my windowsill!

In the meantime bird catching nets are still being sold.