Lit Could they co-exist?

It never works because Sith are selfish power hungry and immoral and Jedi are peace keepers that stop the above mentioned.

 

Maybe there should be a Force Olympics every four years just to give the pent up rivalry an escape valve. Everyone could get medals and have drinks afterward.

 

I have to agree

 

What were the Sith doing for the last 1000 years, in which they managed to avoid drawing the Jedi's attention?

 

It's more about the instauration of a more efficient society, this is not as manichean than you said :

A Sith wants Order, Pyramidal Hierarchy even if it's lead to Injustice.
A Jedi wants Freedom, Justice even if it's lead to Chaos.

This can lead to a convergence of interests, but often leads to conflicts between the two because the ideal society is not the same for the two organizations.
So in my opinion, the confrontation between Sith and Jedi is not a matter of good against evil, but about the divergence about the means to employ to achieve the objective of both organization.

 

I hate the idea of the galaxy being unable to get past the Jedi-Sith conflict.

 

I would hope one day they could reach a higher sense of enlightenment and learn to coexist. But would they still be Jedi and Sith?

 

I'm not sure you can say that with utter certainty.
Most sith seem to just want power/destruction, although Palpatine certainly fits your description.