I might be able to create a situation where the Cult is using a publicly popular front organization to do things that they might not be able to do directly. But given that we are talking about a god of Disease, Death and Suffering, I am not convinced I can have the cult ever act openly and be accepted by a functioning society.
END COMMUNICATION
A way a front for the cult might gain some popularity or standing is as experts on the thing they ultimately wish to spread, namely disease and infection.
A small group could work with clerics researching the very disease others in their organisation is spreading. Once this team has had a small initial success (to gain their credantials) they could then actually work to subtley hinder or divert other clerical attempts to cure the disease.
They could request specialised ingrediants and reagents that are only found in dangerous places then try and get important clerics assigned to teams that are tasked to gather them. The cult could make sure that these adventuring teams meet heavy resistance. This could be a way for the PCs to get involved by forming the backbone of one such team on an important mission.