You cannot cross a C3 without declaring war on it. On the other hand, there is no penalty to declare war on it. Simply, declare war on the C3 and move across it at will. There is nothing the C3 can do about it.
For a player country, you can move across it if the player gives you permission. Check the war page for the link "allow foreign units". You also automatically have access if they are a member of the same federation. Of course, you can also declare war if the target meets a long list of requirements (war level/not secured/not temporary war protection). There is also the possibility the player will shoot back.