The Hatch Act became Federal Law in 1939 and was initially proposed by Republicans as a means of countering what they saw as excesses by (Democratic) Roosevelt administration appointees accused of meddling in local elections.

The Office of the Special Counsel is an independent organization created by law in 1979 to protect whistleblowers from retaliation and ensure that there was not improper influence by the executive branch in elections and campaigns.

Enforcement of the Hatch Act has nothing to do specifically with Democrats and Robert Mueller has nothing to do with the Office of the Special Counsel.