Kazhdan's property (T) vs. residual finiteness

Rufus Willett and Guoliang Yu, MR 3246936 Geometric property (T), Chin. Ann. Math. Ser. B 35 (2014), no. 5, 761--800. showed that if a finitely generated group is residually finite and finite quotients of the Cayley graph have ``Geometric Property (T)", then the group has property (T). A residually finite group has property $(\tau)$ if finite quotients of the Cayley graph are expanders, and it is known that there are groups which possess property $(\tau)$ but not property (T). So this condition on a sequence of finite graphs is stronger than just being expanders, and it is a property holding under a very coarse equivalence relation.

Perhaps it's worth mentioning that Property (T) seems to repel certain strengthenings of residual finiteness. An open question of Long and Reid asks:

Is there an infinite finitely generated group which is LERF and has Property (T)?

Recall that LERF stands for Locally Extended Residually Finite, and means that every finitely generated subgroup is closed in the profinite topology. (Residual finiteness means the trivial subgroup is closed)

Long and Reid's question may have a positive answer, but the point of it is that such groups seem in any case to be extremely rare and/or difficult to construct.