Is it possible to ride in sync with a friend.

Yes it is. It is BeamMP after all. Are you experiencing any kind of problems or sync issues?

My friend and I have different actions while being on the map.

What server are you joining? Have you tried other servers? Do you have an antivirus? Try allowing BeamMP through your antivirus and windows firewall. Usually sync issues are caused when you are not sending or receiving the correct or appropriate amount of data, so something could be blocking it.