As it's a triggered ability, your opponent can respond to it when that player receives priority, just as they can respond to you casting the Shielded by Faith in the first place.
Shielded By Faith's ability is triggered. You can tell because it starts with "whenever"; all abilities that start with "when", "whenever" or "at" are triggered and use the stack (with one exception: if they produce mana and trigger from a mana ability, they are also mana abilities so they don't use the stack).
So, when the Ornithopter enters the battlefield, the Shielded's ability triggers and goes to the stack. Your opponent can then respond to this ability by removing the Ornithopter. If they do, Shielded stays where it is, attached to the other creature.
Note, that the choice to attach Shielded by Faith is made upon resolution of that trigger. This means, that your opponent has to respond withpout knowing wether or not you want to attach the aura to the new creature. So he can respond to the trigger but not to the choice offered by it. He cannot wait to see what your choice will be.
So, when the Ornithopter enters the battlefield, the Shielded's ability triggers and goes to the stack. Your opponent can then respond to this ability by removing the Ornithopter. If they do, Shielded stays where it is, attached to the other creature.
Does this mean that by removing the Ornithopter before the trigger resolves, the option to attach the aura to it is also removed, even if the goal was to get rid of the aura?
So, when the Ornithopter enters the battlefield, the Shielded's ability triggers and goes to the stack. Your opponent can then respond to this ability by removing the Ornithopter. If they do, Shielded stays where it is, attached to the other creature.
Does this mean that by removing the Ornithopter before the trigger resolves, the option to attach the aura to it is also removed, even if the goal was to get rid of the aura?
Even if there was no 'may' and moving Shielded by Faith was mandatory, it wouldn't budge if the new creature was removed in response to the trigger. An aura that's attached to a permanent cannot move to a permanent that no longer exists. That instruction being impossible, nothing happens, so it stays where it is.
303.4j. If an effect attempts to attach an Aura on the battlefield to an object or player it can't legally enchant, the Aura doesn't move.
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Does this mean that by removing the Ornithopter before the trigger resolves, the option to attach the aura to it is also removed, even if the goal was to get rid of the aura?
The triggered ability will still get to resolve; it's just that the player can't choose to attach Shielded by Faith to Ornithopter since it isn't on the battlefield anymore (C.R. 608.2d, 701.3a), so Shielded by Faith won't move. (Even if Shielded by Faith had merely said, "...enters the battlefield, attach Shielded by Faith..." -- that is, without offering a choice -- the result would be the same: since it's impossible to attach it to a creature that isn't on the battlefield anymore [C.R. 701.3a], that effect is ignored [C.R. 101.3] and Shielded by Faith won't move.)
If Shielded by Faith is already on the battlefield attached to a creature (i.e. Angelic Wall) then you play a second creature (i.e. Ornithopter) and you decide to attach Shielded by Faith to Ornithopter. Would your opponent be able to destroy your Ornithopter with a Lightning Bolt before Shielded by Faith attached or does attaching Shielded by Faith happen simultaneously as Ornithopter enters the battlefield.
P.S. This is my first post so apologies in advance if I broke any rules or asked a noob question.
I̟̥͍̠ͅn̩͉̣͍̬͚ͅ ̬̬͖t̯̹̞̺͖͓̯̤h̘͍̬e͙̯͈̖̼̮ ̭̬f̺̲̲̪i͙͉̟̩̰r̪̝͚͈̝̥͍̝̲s̼̻͇̘̳͔ͅt̲̺̳̗̜̪̙ ̳̺̥̻͚̗ͅm̜̜̟̰͈͓͎͇o̝̖̮̝͇m̯̻̞̼̫̗͓̤e̩̯̬̮̩n͎̱̪̲̹͖t͇̖s̰̮ͅ,̤̲͙̻̭̻̯̹̰ ̖t̫̙̺̯͖͚̯ͅh͙̯̦̳̗̰̟e͖̪͉̼̯ ̪͕g̞̣͔a̗̦t̬̬͓͙̫̖̭̻e̩̻̯ ̜̖̦̖̤̭͙̬t̞̹̥̪͎͉ͅo͕͚͍͇̲͇͓̺ ̭̬͙͈̣̻t͈͍͙͓̫̖͙̩h̪̬̖̙e̗͈ ̗̬̟̞̺̤͉̯ͅa̦̯͚̙̜̮f͉͙̲̣̞̼t̪̤̞̣͚e̲͉̳̥r͇̪̙͚͓l̥̞̞͎̹̯̹ͅi͓̬f̮̥̬̞͈ͅe͎ ̟̩̤̳̠̯̩̯o̮̘̲p̟͚̣̞͉͓e͍̩̣n͔̼͕͚̜e̬̱d̼̘͎̖̹͍̮̠,͖̺̭̱̮ ̣̲͖̬̪̭̥a̪͚n̟̲̝̤̤̞̗d̘̱̗͇̮͕̳͕͔ ͖̞͉͎t̹̙͎h̰̱͉̗e̪̞̱̝̹̩ͅ ̠̱̩̭̦p̯̙e͓o̳͚̰̯̺̱̰͔̘p̬͎̱̣̼̩͇l̗̟̖͚̠e̱͉͔̱̦̬̟̙ ̖͚̪͔̼̦w̺̖̤̱e͖̗̻̦͓̖̘̜r̭̥e͔̹̫̱͕̦̰͕ ̗͔̠p̠̗͍͍̱̳̠r̰͔͎̰o͉̥͓̰͚̥s̟͚̹̱͔̣t͉̙̳̖͖̪̮r̥̘̥͙̹a͉̟̫̟̳̠̟̭t͈̜̰͈͎e̞̣̭̲̬ ͚̗̯̟͙i͍͖̰̘̦͖͉ṇ̮̻̯̦̲̩͍ ̦̮͚̫̤t͉͖̫͕ͅͅh͙̮̻̘̣̮̼e͕̺ ͙l͕̠͎̰̥i̲͓͉̲g̫̳̟͈͇̖h̠̦̖t͓̯͎̗ ̳̪̘̟̙̩̦o̫̲f̙͔̰̙̠ ̹̪̗͇̯t͖̼̼͉͖̬h̹͇̩e͚̖̺̤͉̹͕̪ ͚͓̭̝̺G͎̗̯̩o̫̯̮̟̮̳̘d̜̲͙̠-̩̳̯̲̗̜P̹̘̥͉̝h͍͈̗̖̝ͅa͍̗̮̼̗r̜̖͇̙̺a̭̺͔̞̳͈o̪̣͓̯̬͙̯̰̗h̖̦͈̥̯͔.͇̣̙̝
So, when the Ornithopter enters the battlefield, the Shielded's ability triggers and goes to the stack. Your opponent can then respond to this ability by removing the Ornithopter. If they do, Shielded stays where it is, attached to the other creature.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)
Does this mean that by removing the Ornithopter before the trigger resolves, the option to attach the aura to it is also removed, even if the goal was to get rid of the aura?