There's plenty that could be said but the short version is Luke Abrams urges those who are at Mars Hill to vote with their checkbooks and be willing to withhold tithes until the executive elders appreciate a need for changes in policy. Luke would be in a better than average position to have seen what went on behind the scenes in the leadership culture than average.
For those who might propose (as at least one commenter has at Throckmorton's blog) that withholding tithe money is bad, the alternative can be worse. Suppose you gave 20% of your income to support, say, the Lake City Campus only to see the executive leadership decide to just shut the campus down with a public explanation of a lack of numbers in attendance or giving when internally there was evidence that Lake City had the highest per capita giving of any campus.
In case you're not inclined to believe this, here's a post on the Lake City campus from the real estate and mars hill series of posts. Mars Hill members have been asked to give sacrificially in settings where the campus they gave to got shut down anyway. It's not impossible that campuses may have tried to get together funds to keep people on staff that executive leadership just decided to cut loose regardless of whether or not there was local campus funding available to keep someone employed. Mars Hill has all the top-down power-play structure you might expect to see in a denomination but with none of the positive benefits of local church autonomy and the opportunity to customize teaching from the pulpit to address what may be going on in a given actual community.
So if Luke Abrams suggests you vote by either not attending or withholding tithe, that's certainly your call.