There is a difference between a false teaching and a false gospel. I believe synergism propagates a false teaching in its understanding of God's sovereignty and human responsibility. That false teaching does not necessarily result in a false gospel. Many synergists believe salvation is still by grace through faith in Christ alone. I am thankful for that happy inconsistency. Monergism preaches the same gospel. It differs over God's primacy in election. It creates heated debates between both camps, and broken fellowship, but it does not add works to the gospel. If you believe it does, then with all due respect, that is a problem you will have to work out.
Romanism adds works to faith. That is not just a false teaching, it is a false gospel that lacks the power to save.