Actally, you were correct in your response to my post as I didn't know they would have to employ an outside lobbyist to represent them at the time of my post. Now I see how the game is rigged with ways to get around the spirit of the law.
Yes, what they as a not-for-profit/church are prohibited from doing, under any circumstances, is providing monetary support to any candidate or political party.
In actuality, if one reads the Charter of COSRECI, that South Australian not for profit that is the umbrella of operation for the "churches" throughout the British system (UK, Oz, NZ etc.) it's charter and by-laws actually state it is to not engage in political lobbying.
It is possible there is a subtle nuance of difference between the two legal systems cum definitions of "lobbying." I quite often find myself having to be careful which legal standard I am applying when I think/write on all sorts of subjects: not just this subject. Accounting and also Tax Law are examples where there are differences.
Dulloldfart, Mate and I and discoursed on ESMB on this COSRECI issue earlier in the year in the run up to the Oz Senate hearing.