Is ἄρσις etymologically related to άρσεν (male = active sex) and θέσις etymologically related to θήλυ (female = passive sex)?
What a coincidence, but they're actually unrelated.
ἄρσην ("male") is the Greek form of an old Proto-Indo-European word *uers-n-, with plenty of cognates in IE languages. It is actually related to the Latin verres 'ram' and other words in Sanskrit, Armenian, and Lithuanian referring to the male of an animal's species.
Meanwhile, ἄρσις comes from ἀείρω meaning "to raise up." An ἄρσις is thus a raising. The exact etymology of ἀείρω is uncertain, but Beekes reconstructs the PIE form as *h2uer-, which as you can see is a very different looking form.
θήλυς and θέσις follow a similar trajectory. The former is derived from the PIE **dheh-*, which means "to suckle." It is etymologically related to the Greek θηλή ('nipple') and the English female (from the Latin femina).
θέσις instead is derived from the verb τίθημι, and means "a placing" or a 'setting down.' It is actually where we get the English "thesis" from, as a 'topic set down [for discussion].' (Notice in fact the parallelism with the English position, from the Latin positio, meaning 'a setting down, a placing.')
So no, they're not directly related, but what might be interesting to explore is whether these were the words chosen because of their similarities to 'male' and 'female.' That I don't have an answer for, at least not without reading every place they're discussed, but I suppose it is possible.