Moss is a good addition to the compost and it will not necessarily spread to areas where that compost is used. Moss is a first stage plant that grows most often in soils with very low levels of organic matter. Since adding enough compost, an other forms of organic matter, increases the level of humus in the soil moss won't grow in that environment.

Well okay then- looks like I'll be composting the front yard.
Thanks for the response.

Also, moss favors acid soil. You may want to get a soil test and work on raising the PH, depending on what you are planting next.

Increased pH doesn't decrease moss.

You have moss because your climate is moderate and moist; your soil is compacted; and your front yard has excess shade.

I keep seeing this "moss favors acid soil" and I keep seing moss growing on concrete blocks (lime), concrete sidwalks (lime), my crushed dolomite rock (lime) covered driveway, and other, similar, places. So why is that if moss favors acid soil?

I say this because I just read it on a fact sheet on "moss in lawns" we send out from the county extension office (I am a volunteer). And from my own experience, I have moss that grows in full sun in my so called "lawn". The soil there as been tested and is acid. I don't have the figure handy but lime has been recommended to grow grass.

I do believe the fact sheet did say that increasing the ph will not get rid of the moss. As we can see, moss seems to grow everywhere. But is makes sense to me that having the ph at the correct level for the desireable plant(s) will help squeeze out moss.

So getting a soil test is always a great way to begin.