Actually, the rooster has theological implications.  I can look all this up again (Google steeple, rooster) but essentially, a pope in the middle ages dictated that a rooster should sit atop a steeple.  In the reaction following the Protestant reformation, the Catholics decided that in a burst of devotion, they would top their steeples with a cross.  This left the rooster as a symbol of the Protestants (especially the Lutherans).  All I know is that our Norwegian scholar sent us dozens of pictures of magnificent roosters atop Norwegian churches--and taught us the special term they had for them.

The practice did not survive the trip to USA very well.  Perhaps it was because by the mid 19th century, there were already thousands of weathervanes on barns, etc. that used roosters.  This would explain why the folks off the boat put a rooster on their church but a generation later, their children would probably think the practice corny.  By the time I came along, the practice was virtually unheard of.

When I was first in Europe in 1970, I was so surprised to see a rooster on a church in northern Germany , I actually asked how a barnyard animal came to represent religious devotion.   That was the first time anyone had explained to me how a rooster would symbolize which side of the 30 Years War one found oneself at the end of hostilities.

"Remember the I35W bridge--who needs terrorists when there are Republicans"