OK, I admit I picked my subject line to be deliberately controversial. The controversy is this: how much does any person contribute to the work of salvation done in their everyday lives?
The 'hard' Reform guys say - it was God, beginning to end, and any person saved has no input or influence on God's sovereignty. There was only "one worker" (mono+erg = monergism).
The other Reform guys (remember that Arminius and Weslyans are also part of the Reformation) say - yep, God did all of the heavy lifting and that much is clear. But at some point we (as a response to God's working and 'wooing') had to grope a bit and come to some conclusion and then decide. That is, God and the person "together worked" (syn+erg = synergism, "synergy" is a similar idea). Now the reason hard Reform guys don't like 'synergism' is they get very allergic (and for very good reason!) to anything that smells like Pelagianism. It's not the heresy of Pelagius, but it can sound like that.
OK, now that's the issue with our justification. That is, justification is the work of conversion that occured when we were saved, converted, regenerated, etc. For the Christian alive today, justification is in the beliver's past.
So the open issue that this text seems to present is what about our sanctification? That is, the work that God does in our every-day present lives to transform us to be more like Jesus. For the Christian alive today, sanctification is how God continues to daily 'save' us from our past life, habits, etc. Is this spiritual work done only by God (monergism) or something we partner up with God about (synergism).
This text seems to speak against 'synergism' - that we shouldn't be 'perfected' (sanctified) by any work of our 'flesh.'
But I don't think that's the issue. I think that the issue in that text is that the Galatians were getting confused about was whether they needed some extra physical (flesh) rite to "seal the deal" (perfect) their justification. In a rough analogy to what the Roman Catholics believe, that there is a two-stage justification (gotta do good works to seal the deal), so the Galatians believed they needed to do Jewish rites to seal the deal. That, BTW, goes *way* beyond 'synergism!' Theologically, as to what the Galatians were proposing; well that just takes you right off the reservation of Christianity (Protestant, Roman, or Orthodox) - which is precisely Paul's point. Believing you need to do Jewish rites (be circumcized) to "seal the deal" of your justification is heresy.
Nope, this test isn't about sanctification, it's about justification. Paul is trying to get them back to the gospel: you have been completely saved, actually sealed by the Spirit, and as that work was completely done in the believer's past there's nothing else that the believer can do to improve upon their justification.
Now, as to your sanctification, Paul has stuff to say about that. For example, serve each other (5:13), walk with the Spirit (5:16, and keep in step with the Spirit (5:25).
So the point of Galatians 3:3 is not about monergism or synergism in our sanctification, but about a heresy of justification.