I mentioned Dobson's recently-founded 501(c)(4) group a while ago, and it looks like a clear reason for him to oppose campaign finance reform is his own organization.
The main thrust of campaign finance reform since the '90s has been targeting soft money. Soft money is contributed not directly to a campaign or candidate, but to a PAC like Dobson's, which then have very little regulation or disclosure requirements with the public. It's basically a way to try to buy elections, and the Supreme Court agreed in 2003 to uphold limitations on soft money. While I agree that our constitutional civil liberties must be protected, the issue is being obfuscated in much the same way that church-state issues are (by the same players): the Constitution protects individual liberties, not those of PACs. While I personally have the right to say and do as I wish with respect to advertising and campaigning for a candidate, the state has a vested interest in regulating the activity of collective efforts backed by corporate dollars.
Any time that transparency mixes with politics, those who practice in the dark fight furiously against the intrusion of light. We should be quite suspicious of those who are so vocal and adamantly opposed to this legislation via sheer demagoguery (using lies about limits on individual religious expression).
I don't actually think that Dobson wants to hide something of his own personal fortune. I mean, hell, Dobson only makes around $300 K himself in his $200M FoF empire (plus $30M for the FoF "Action" political branch), just chump change, really. I think the real fear that these people have is the way that the money flows from their non-profit religious groups to their political action groups. That, combined with who is funding those action groups. I think Dobson doesn't want the public to know that he is bankrolled by the same machinations that Ralph Reed, with the Christian Coalition, was: Jack Abramoff and crooks just like him. I think Dobson and Perkins and others like them are in bed with the same corrupt lobbyists that all the politicians are, and they don't want anyone to know about it. The money they receive from their religious fronts are siphoned over to PACs. They are able to take politicians out to dinner and on trips to influence their votes for their own special interests. Dobson and his ilk are no better than any other politicians or lobbyists in DC, they just don't want anyone to know about it.