How to reduce moss growth on lawns without toxic chemicals?

You an poer wash it off depending on where it is or

Vinegar

Vinegar contains acetic acid, weak enough for humans to consume but strong enough to kill moss.  To use, simply pour white vinegar directly on the moss and let sit for 30 minutes. Rinse or scrape the moss away. The downside is that depending on your area of moss coverage you may need to purchase lots of vinegar. And you’ll want to make sure that the vinegar doesn’t get a chance to seep into surrounding plants as it will negatively affect their health. Some roofing experts don’t recommend using this product on your roof.

Homemade Moss Killer

This “recipe” is made from inexpensive ingredients you may already have at home. Combine water, vinegar, salt and soap with the following ratios: 1 gallon of warm water, 1 tablespoon of vinegar, 1 pound of salt and as much soap as you want as long (as it’s not more than 20% of the mixture). Pour the mixture into a spray bottle and spray directly onto the moss. Once the moss has turned brown it’s time to scrape it off the surface and discard. As you can imagine, this moss killer will also kill other plants so use caution when spraying.

http://porch.com/advice/hot-to-remove-moss/

Spunky has it about right.  On the other hand moss growing on your lawn usually means your soil is depleted and/or lacking organic matter.   Can also be a sign of  fertilizer salts build up if you or previous owners used synthetic fertilizers like Tru-Green  services or Miracle-Gro style lawn fertilizers for years.
If don't fix your soil the moss will usually return and grass won't grow well.   First don't remove leaves and grass clippings.   Mulch them into the lawn with your lawn mower.   That helps keep the carbon and adds organic matter.   Second spread a high nitrogen  fertilizer.  Moss gross and takes over in low or unavailable nitrogen soils.   Preferably a solid organic based fertilizer.   Aerating your lawn then spreading a  generous amount of composted cow or horse manure ( not fresh stinky stuff,   black dirt stuff  from the garden center) over the lawn so it can work it's way into the aerated soil.   It will probably take repeated applications but eventually the soil will be corrected enough that grass will grow well and be inhospitable to moss.

Good luck.

I just dealt with a patch in my lawn that was almost entirely moss.. I am assuming you tried the old fashioned way of raking it carefully? That tends to pull out the moss but leave the grass..  You can then reseed . as I have just done... it was part of a swathe that has been reseeded

oooh if it helps, I have a plastic rake - it seems to damage the grass even less than a metal one...mine's part of the Wolf fit together system... I love that set up... and the fact you can have different size poles for each of the heads ... so the rake is a plastic but very well made head that fits on a wolf pole..

The aeration that someone else suggested was a good suggestion as moss tends to occur in damper areas in my case it was damp and shade... so I do have to watch that.

I used to garden for a living.. but lawns were never my fav thing.. if I were nearer I'd offer to help but in my absence I am sure you will do a great job... Good luck with it and thank you so much for giving us a chance to talk about something other than politics.. I mean I do answer many politics questions but it really isn't a very positive experience sometimes :(

The best but hardest way is to rack it out with a moss rake. Also if you get a piece of 1/4 inch pipe and make a bunch of holes about 4 inches deep and a foot apart then fill the holes up with clean sand it will help keep the moss down. Vinegar will kill your lawn. Cheers