The flip chance of Hispalis is currently 0.087%. 4 turns after rushing the temple, the flip chance would lower to approximately 0.03% (this assumes the garrison remains at 2). Note that the borders of Cattaraugus are unlikely to change other than that one nearby tile at cultural distance 3 until it is captured. Rushing the temple would also allow Hispalis to work a floodplain tile, a desert tile, a hill tile, a grassland tile with fur, and 3 sea tiles. Note that Hispalis has 92% corruption and needs a courthouse to be able to produce more than one shield (or maybe planting a forest on that grassland tile or something would allow 2 spt).
Therefore, I believe the furs are the primary reason for the rush. The cost is indirectly less than it seems, since it will free up garrisoned troops, and avoid the use of specialists and the lux slider. I think waiting a little while to rush the temple would be okay. A possible plan would be to upgrade first, then rush the temple when it's cheaper. Or we could build LW as classical_hero suggests, delaying the upgrades (I don't want to delay them for that long, however). The impact of the furs would be felt immediately, however. I wonder it could put any cities into WLTKD? Immo, Zojoji, Regent Town, and Corrino (Regent Town and Corrino would grow to 6 by the time the furs were in our culture), perhaps?