So it's actually by the first definition I found, mutual does literally mean reciprocated, not for both A and B to have the same feeling, but for A to feel about B as B does bout A
(of a feeling or action) experienced or done by each of two or more parties towards the other or others.
The second definition it gives is what they're going for though no
held in common by two or more parties.
"we were introduced by a mutual friend"
So I suppose they want to use that in reference to ""
Feel buying your first home shouldn't be impossible? The feeling's mutual" - In other words both hold in common the idea that it shouldn't be impossible to buy a first home.
Obviously they ought to know about the meaning seeing as it's their name.