There are very good reasons for attempting to reduce antibody numbers.
Antibody numbers and activity fluctuate a lot. Antibodies attack the thyroid, destroying the cells it is made up of. It may take years or even decades, but the thyroid will eventually be destroyed. People on the forum who have had scans of their thyroids after many years of Hashimoto's Thyroiditis (aka autoimmune thyroid disease) have said their thyroids appear to be wizened little lumps, often no longer capable of producing any thyroid hormone at all.
So, the first reason for trying to reduce thyroid antibodies is because it makes the thyroid last longer.
Secondly, when antibodies kill cells in the thyroid, any thyroid hormone contained within those killed cells is released into the body. These hormones can often be plentiful enough to show up in substantially altered Thyroid Function Tests. The patient concerned may end up, temporarily, severely over-dosed on thyroid meds such as Levothyroxine. If tests are done at the time of a flare-up of antibody activity then people may find themselves having their meds reduced, or removed, or in the worst case scenario, they may be told they are hyperthyroid and they need to go on thyroid suppressing drugs.
[Although it wasn't in the context of antibody activity, Dr Barry Durrant-Peatfield, in his book Your Thyroid and how to keep it healthy has written about having to intervene to prevent people having their thyroids removed because blood tests showed high Free T4 levels when the patient was obviously hypothyroid. See second Edition, page 79]
Because antibody activity, and therefore blood test results, fluctuate a lot, people find themselves frequently wrongly-dosed on their medication. They may end up on beta blockers, suffering heart issues such as tachycardia and palpitations. The mental and physical effects of fluctuating thyroid levels are hard to cope with.
So, any doctor who thinks that antibodies are unimportant is a callous idiot.
There aren't any definitive treatments for lowering antibodies, so people have to use trial and error to find what works for them.
What helps some people :
1) Taking 200mcg selenium per day.
2) Switching to a gluten-free diet. Even if the patient has been thoroughly tested and been found not to have coeliac disease, giving up gluten reduces antibody numbers a lot for some people. It has to be done ruthlessly though. Giving up gluten only occasionally is utterly pointless.
3) Switching to a diet which excludes animal milk products. The offending substance in these products could be lactose or casein or both.
4) Giving up nightshades - there are lots of lists of nightshades available on the web.
5) Dramatically reducing sugar in the diet.
I'm sure there are other dietary interventions people have tried. The important thing is to only try one intervention at a time, and if it makes no difference then put the food you've been excluding back into your diet again, otherwise the diet becomes far too restricted.