It is a problem. The 501(c)(3) organization, Planned Parenthood Federation of America has a Board of Advocacy whose activities included lobbying of elected officials. Most of their political activity is done through a 501(c)(4) organization called Planned Parenthood Action Fund. As a 501(c)(4) organization, donors would be disclosed to the IRS, but not publicly.
The point is, an at-will employee with a super religious boss might be legitimately concerned about his name showing up on donor lists for organizations that advocate for abortions or gay marriage. Similarly, a gun rights activist might be concerned about his name showing upon on donor lists if his current boss lost a child to a gun crime and is a vigorous advocate in opposition to gun laws. There is also the possibility that a future employer could check donor lists during the hiring process. It doesn't really matter if such behavior is legal, it would be extremely difficult to prove and we shouldn't force people to be public advocates if they want to support controversial issues.
If Martin Luther King Jr. could have obtained more donations for the Civil Rights Campaign by setting up an organization to get anonymous donations, that is a good thing, not a bad thing.