The name may be civil, after Augustine, taken from the heavenly city rather than the earthly
What the honor is called matters less to them than what it consists in and how it is shown.
They refuse the bare name religious, because religion properly looks only to God's cult.
They prefer civil, or Augustine's phrase, a cult of fellowship and love.
Civil here is taken from the heavenly city of grace and glory, and it still outranks earthly civic respect in degree.
Latin
XII. Quo vero nomine sit honor iste signandus, parum referre existimant; dummodo de re ipsa constet, quibus, scilicet, in rebus ille constituendus sit, & quibus actibus & signis testandus atque exhibendus. Nolunt tamen simpliciter Religiosum dici, quoniam religio solum cultum divinum proprie & directe spectat; sed potius civilem, vel ut loquitur Augustinus, societatis & dilectionis. Non quod eum confundant cum illo cultu quem civilis dignitas, & naturae quaedam praestantia requirit: hunc enim, ut dictum, gradu saltem superat. Sed cum duplex sit civitas, una terrena, & altera caelestis, civilem dici posse putant denominatione sumpta, non a civitate terrena, sed caelesti, ad quam pertinet gratia & gloria, cui cultus & honor ille deferendus est.