You cannot cast a spell during the resolution of a spell unless that spell specifically instructs or allows you to. Worldpurge is currently resolving in your scenario as indicated by players making decisions as prompted by the spell's effect. They do not make those decisions earlier than that. Also, you as the active player make the choices first. The decision making doesn't come around to you, it starts with you.
You can cast Teferi's Protection in response to Worldpurge. But that is then also before anything is bounced and any decision about what to keep is made. Because to respond means to act before the thing you are responding to starts resolving. As the player who has cast Worldpurge you are in fact the player who gets to respond first. But if you don't respond then and there, and no other player responds, the spell resolves. That is the risk you take when passing instead of responding immediately.
You cannot cast a spell in the middle of another spell resolving. You could cast Worldpurge, hold priority and then in response cast Teferi's Protection to phase yourself out.
In general, you can cast Teferi's Protection in response to Worldpurge, because the player who had priority after casting a spell gets priority back, and because Teferi's Protection is an instant (C.R. 601.2i, 117.1a).
Note, however, that in a sanctioned tournament, if the player with priority adds an object (such as Worldpurge) to the stack, that player is assumed to pass unless that player announces that they're retaining priority. In this sense, if you're assumed to pass this way, all other players can choose to pass as well, so that Worldpurge will resolve and return all permanents to their owner's hands (and do the rest of its effect). See also this thread.
Certain people are telling me I cannot cast TP in response to WP. I say that I can. Who is right?
The timing for responding to a spell is somewhat trickier when you wish to respond to your own spell.
Responding to another player's spell is straightforward: they play some spell, you respond by saying 'wait! before it resolves, I will play...'
If you wish to respond to a spell of yours, you must be cautious:
eiher you immediately say 'hold on, I wish to add some more', immediately after casting Worldpurge
or
you wait for other players' responses, but that is a risky move: if no one responds, then Worldpurge WILL resolve as you won't get another chance to respond to it.
That's because, since you did wait for other players to repond, it actually implies that you meant 'I pass'.
If everyone else also say 'I pass', then all players have passed in succession (including you), therefore the spell resolves here and there:
117.4. If all players pass in succession (...), the spell or ability on top of the stack resolves (...)
So if I read correctly, if I’m the active player, I can cast Wrath of God, hold priority and cast TP and avoid having my creatures blown up
correct?
In effect. This is because once the permanents you control phase out due to Teferi's Protection, they won't be "visible" to Wrath of God (just as they won't be "visible" to Worldpurge) (C.R. 702.26b), so that it won't destroy any of them even if they're creatures.
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Teferi's Protection
In a game I cast World Purge and when it gets back around to me I cast Teferi's Protection.
Certain people are telling me I cannot cast TP in response to WP. I say that I can. Who is right?
You can cast Teferi's Protection in response to Worldpurge. But that is then also before anything is bounced and any decision about what to keep is made. Because to respond means to act before the thing you are responding to starts resolving. As the player who has cast Worldpurge you are in fact the player who gets to respond first. But if you don't respond then and there, and no other player responds, the spell resolves. That is the risk you take when passing instead of responding immediately.
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Note, however, that in a sanctioned tournament, if the player with priority adds an object (such as Worldpurge) to the stack, that player is assumed to pass unless that player announces that they're retaining priority. In this sense, if you're assumed to pass this way, all other players can choose to pass as well, so that Worldpurge will resolve and return all permanents to their owner's hands (and do the rest of its effect). See also this thread.
EDIT (May 16, 2021): Add rule citations.
Responding to another player's spell is straightforward: they play some spell, you respond by saying 'wait! before it resolves, I will play...'
If you wish to respond to a spell of yours, you must be cautious:
eiher you immediately say 'hold on, I wish to add some more', immediately after casting Worldpurge
or
you wait for other players' responses, but that is a risky move: if no one responds, then Worldpurge WILL resolve as you won't get another chance to respond to it.
That's because, since you did wait for other players to repond, it actually implies that you meant 'I pass'.
If everyone else also say 'I pass', then all players have passed in succession (including you), therefore the spell resolves here and there:
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules
correct?