In order for that to happen, you would need to build a relationship with your Vote Buddy. The site can't do that for you so the responsibility is on the person willing to take this up.
You are right that the other person you partner with can agree but later break their promise. Therefore, if your state has it, the best way would be to utilize mail-in ballots, meet one day with your Vote Buddy cast your votes in front of them and then place your ballot in the envelope and mail it in in front of each other at a mailbox or have someone you both trust do it for you.
A couple of people I know do this already and it wors well for them.
The second time the Dem. votes will cancel the deal.
For such vote trading, the vote has to be legally [i.e. its alienation must be contract enforceable] alienable. The problem of trust would surface anyway, but it can be handled in small groups, where unwritten custom instead of a formal law can with difficulty be enforced. On large scale it is not going to work, for I would not trust anyone, myself included - but I'd trust others even less than that.