In Romeo and Juliet, why has "Civil blood ... made civil hands unclean"?

The quote is taken from the prologue to Act 1 and, in part, reads as follows:

Two households, both alike in dignity,In fair Verona, where we lay our scene,From ancient grudge break to new mutiny,Where civil blood makes civil hands unclean.From forth the fatal loins of these two foesA pair of star-cross'd lovers take their life;Whose misadventured piteous overthrowsDo with their death bury their parents' strife...

The prologue...

The quote is taken from the prologue to Act 1 and, in part, reads as follows:

Two households, both alike in dignity,
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
From forth the fatal loins of these two foes
A pair of star-cross'd lovers take their life;
Whose misadventured piteous overthrows
Do with their death bury their parents' strife...

The prologue informs of a battle raging between two families. The two households are equal in stature and power and their 'grudge' is the ill-will that they bear one another. The antagonism between these two houses has been going on for ages and has now, once again, sparked battles between the rivals. These fights are disrupting the peace and have brought unnecessary turmoil to the beautiful town of Verona. 

The hatred of the families for each other has resulted in blood being spilt, due to the fighting. 'Civil blood' alludes to the fact that the blood of ordinary citizens has been shed, either because they were drawn into the fights or that they have been injured whilst being innocent bystanders. It could also mean that they retaliated when confronted by those loyal to either of the two families or that they were forced to defend themselves against attacks by the unruly members of both households.   

'Makes civil hands unclean' suggests that ordinary, respectful and well- behaved citizens who respect the law have also been affected by the antagonism and aggression displayed by the feuding families. It indicates that they have become unfortunate participants, unwittingly or not, in this continuing war and have themselves shed blood as suggested above, either in self-defence or due to the provocative nature of the upheavals which inspired them to join in. 

The prologue says that two lovers, each from one of the families, destined to be together, are caught up in this strife and become its victims. They end up taking their own lives. Their deaths ultimately make the two families realise that their feud has no purpose other than to destroy them. They then resolve their differences and agree to end their destructive and purposeless fight.