Since till now the conversation between Radhika and Shantanu is not yet exposed, but the only thing I observed is Bhrigu shastra(if I got it correctly). I think Shantanu is a reincarnation of someone in Purohit family who suffered due to some wrong decision made in the past. He might be related to chacha i.e my point is chacha's father who might be the actual heir of the property but did not become heir due to some incompetence. Like in Mahabharata, there was always a stress in the relationships of Kauravas and Pandavas as to who is the right heir, because Pandu instead of being younger son became the king since he was a healthy child. Dhritrashtra being blind had to forfeit his claim to his throne because of his blindness.
All these grudges between the two branches ultimately led to the war of Mahabharata since the sons of Pandu and Dhritrashtra always had a question who actually is the right person and actually owns the throne.
Today looks like the old question of Purohits is coming back where Dev is today RajPurohit (like pandavas) but somewhere in the past someone else might had to forfeit his rights. Shantanu might be either related or a reincarnation and is now claiming for those rights again.
Thats why Radhika was saying that on one hand is Purohit family's reputation and on the other hand is Dev's RajPurohit gaddi (throne).
These are just my thoughts. Please share your thoughts.