27. Are there provisions requiring donations to go through the banking system?

Electoral Act 1997 Section 23B, as amended by Electoral (Amendment) Act 2001 49.  (1) A member of either House of the Oireachtas, a representative in the European Parliament, a candidate at a Dáil, Seanad or European election, a political party, a third party or an accounting unit who or which receives, in any particular year, a monetary donation the value of which exceeds £100 shall open and maintain an account in an institution in the State and shall lodge that donation and any further monetary donations received by him or her or it to that account.

If a candidate, representative, or accounting unit of a political party receives monetary donations of more than €100 in a given year, it and all subsequent donations must be routed through a 'Donations Account' at a financial institution.  The definition of a financial institution includes An Post (the post office) and most banks, building societies and credit institutions. It does not, however, include a credit union. 
See Standards in Public Office Commission. 2017. Guidelines for Members of the Houses of the Oireachtas and Representatives in the European Parliament relating to acceptance, management and disclosure of donations, p. 18; Standards in Public Office Commission. 2015. Guidelines for Political Parties Steps to be taken concerning donations and prohibited donations, p. 18; Standards in Public Office Commission. 2020.  Guidelines for the General Election to the 33rd Dáil 8 February 2020 [Candidates and Election Agents],  p. 15.