I have my bridles made in the uk in English leather, properly tested, maybe not great by vegan standards because they are dead animals, but it is a by product and until the whole world is vegan the leather is there, and it might as well be used.
As for rope, a halter can be sharp and harsh if used incorrectly. I know that rope has no breaking point, so if your horse gets caught up you better hope whatever it's caught on breaks first before the horse does.
I would like to make a vegan version, but currently many of the materials come from India and China and their production has a huge environmental impact, so even if I have the bridles made in the UK, there is still an ethical impact.
People buying cheap leather wear, and even some expensive leather wear, would be advised to check where the leather is from because it is likely to be poor quality and won't last, add to that the tanning processes are awful, putting huge pollution into the environment. I also take into account employment ethics, and cruelty to the animals. Some leather is from questionable sources and may even be horse, dog or donkey!
I do intend on making a vegan version, but it has to be made right, with ethically produced materials, with proper working conditions, and it will be tested and trialled before it is ever offered for sale. It's not a cheap process and will take time. In the meantime I have ethically made, safe, quality bridles, properly tested, kind and gentle, and to be honest I feel proud that I don't compromise on those standards.