I was diagnosed with low sperm counts, anti-sperm antibodies at levels of 95% and have been trying for a baby with my wife for 4 years. Due to the presence of anti-sperm antibodies we were told ICSI was our best option of conception and that natural conception was unlikely. After first IVF failure, we tried natural ways to reduce anti-sperm antibodies. This included acupuncture, eating clean organic meats, and taking out any foods that could cause immunological reactions in my body after speaking to a nutritionist. This meant that my wife and I both cut out gluten, and I also cut out dairy from my diet.
Interestingly, on our second IVF in 4th year of infertility, I noticed a significant drop in my anti-sperm antibodies level to 50%. ICSI failed again and it was a difficult failure to handle. However, to our surprise my wife conceived naturally a couple of months after the failed ICSI, even though we were told it was impossible and unlikely we would have a natural pregnancy.
My advice is, don't wholeheartedly trust the doctors as unfortunately it is about money for them. This can bias their judgements. Also sperm results can vary over time and clinic so it is worth repeating over months or years.
I cannot say if our clean diet, high in organic meats and fish, cutting out gluten and dairy, my wife cutting down her commute to 10 minutes and a less stressful job change for me,... had an impact that can be scientifically proven. However, I think it helped as the doctors couldn't explain the anti-sperm antibody reduction from 95% to 50%.
Also never stop trying for a baby, and the less stressed you are the better. Finally, last but not least, I truly believe in God (as a Muslim) and we made lots of prayers for God to bless us with a child. As all hardships show, once you have been through them you get closer to God, and remember him more, and are grateful for everything in life - especially the pregnancy.
I hope this information will help someone one day, as having anti-sperm antibodies does not mean you will not conceive naturally.