I tend to agree with Phil Sweet in his comment that there is a nuance between take a stand - to mount a determined resistance, and take a stance -to take a position accompanied by various degrees of a defensive or aggressive attitude.
Etymology: < French stance (now only in the sense ‘stanza’: see 4), < Italian stanza station, stopping place, room, etc.: see stanza n.(Show Less)
1.a. A standing-place, station, position.
1532 E. Boner in State Papers Henry VIII (1849) VII. 396 Beyng at a stance, where oon way turneth to the Popes lodging, and the other to the Emperours, the Pope departed from the Emperour.
1862 H. Beveridge Comprehensive Hist. India II. iv. iv. 143 One chapter is devoted to..stances for deities.
This then broadly remained the case until the late 19th century
1 d. In Golf and other games: The position of the player's feet in playing a stroke. Also transferred, the position of the player's body in readiness or in playing a stroke. Similarly gen., a standing attitude or way of positioning.
1897 Outing 30 426/1 The stance, the grip, the swing, that together make up, what they call a good style.
In its turn "stance" then took on the meaning of
e. figurative. An attitude adopted in relation to a particular object of contemplation; a policy, ‘posture’.
1960 Amer. Speech 35 215 An ‘unlinguistic’ stance is evidenced in the view that some variants embody language ‘corruption’.
1977 J. I. M. Stewart Madonna of Astrolabe xx. 277 Moderate regret and underlying unconcern established itself as our public stance.
The 1960 quote above is the first recorded use of "stance" in this sense.
Stand(n.) is somewhat older:
II. Place of standing.
11.a. A place of standing, position, station; also in phr. to take one's stand, poet. to take stand.
a1300 Cursor Mundi 1694 Siþen efter alþernest hand þe meke beistes sal haue þair stand.
1827 Scott Surgeon's Daughter in Chron. Canongate 1st Ser. II. iv. 114 He saw from his lofty stand all the dumb show of gallantry.
The difference is that the figurative use entered the language in the 16th century:
1595 S. Daniel First Fowre Bks. Ciuile Warres iii. cxxv. sig. S2 Nay father since your fortune did attaine So hye a stand: I meane not to descend, Replyes the Prince.
1874 J. R. Green Short Hist. Eng. People vii. §4. 375 He [Philip] was preparing..to take a new political stand as the patron of Catholicism throughout the world.
It therefore seems that the replacement of stand with stance occurred with the popularisation of golf in the late 50s/early 60s.