You have been pitched under or near trees (no other choice) and it's time to break camp. Tree sap and bird poo may be on the outer. What do you do about this? Leave it or clean it off? If the latter, what do you use to avoid damaging the outer? Many thanks for your advice.
Not much in the long run... it'll eventually take its toll.
The correct answer is preventative action. I learned to routinely use a tarp above my tent when in woodlands as it doesn't half make life easier, no excessive dripping noises in rain, no bird mess and substantially less sap damage. Clever positioning as well allows you a bit of extra shelter over the tent doorway and protection to sit relaxing on rainy days without being stuck in an enclosed tent.
It really depends on how well it will come off. First thing in the morning on going home day the tent could well be damp with dew and that might be a good time to try to wipe off any debris, but try not to rub it in and make more of a mess. Try a small area first as they say.
The alternative is to leave it until dry and then see if it will just rub off (gently) or the third option is to do nothing and accept that tents will get dirty and by the time you have shaken it about and packed it away most of the heavy stuff will have been shed, then subsequent trips in both sun and rain will get rid of the worst of the staining.
On going home day if the tent is quite wet in the morning I tend to go round it with a towel and take off the heavy droplets giving it a better chance of drying in the wind and (sun?) before packing it away. This also has the effect of removing any debris.
Some people will say never to wipe your tent with a towel which may have detergent on it as it affects the waterproofing...probably wise but I have never had a problem.
Wash bird's muck off with water. If its dried on leave wet sponge on for minute but it needs to be washed off before packaway. Tree sap leave alone, you will do more harm than good trying to remove it. It is organic so turns to powder & brushes off in time.