You have the opportunity to choose whether or not that creature gets a +1/+1 counter. It comes down to how you order these two triggered abilities involved.
We'll examine giving it the +1/+1 counter first, then examine what you can do differently to makes sure it doesn't receive a counter.
To be clear for those readers who may not be certain: when you take control of your opponent's creature, it will not count as (re-)entering the battlefield, and so does not trigger Cathar's Crusade itself.
Making sure it receives the counter
You cast Zealous Conscripts.
You and your opponent pass priority (in theory), and then Zealous Conscripts resolves and enters the battlefield.
Because someone now receives priority, we check for any triggered abilities that now have to go onto the stack. Zealous Conscripts entering the battlefield has caused two abilities to trigger: that of Cathar's Crusade, and that of Zealous Conscripts. Because they triggered simultaneously, you may put them in whatever order you like:
603.3b If multiple abilities have triggered since the last time a player received priority, each player, in APNAP order,[note below] puts triggered abilities he or she controls on the stack in any order he or she chooses.
You choose to place Cathar's Crusade's ability beneath, and Zealous Conscripts' ability on top (the top one resolves first).
You resolve Zealous Conscripts' ability. Your opponent's creature comes under your control.
Cathar's Crusade's ability resolves and places a +1/+1 counter on each creature you control, including the one you took from your opponent.
If the creature survives to be returned to its owner, it will return with its +1/+1 counter still on it. How nice of you! (This could be a totally appropriate gift to an ally in a multiplayer free-for-all game.)
Making sure it doesn't receive the counter
At step 4 above, we'll make a different choice.
- You choose to place Zealous Conscript's ability on the bottom, and Cathar's Crusade's ability on the top of it.
- Cathar's Crusade's ability resolves first. It grants a +1/+1 counter to each creature you control, which at this point is just Zealous Conscripts and whatever else you already had.
- Zealous Conscript's ability resolves, and you take control of your opponent's creature. It gets no counter.
Note: "APNAP" stands for "active player, nonactive player(s)". APNAP order means the active player does their thing, then each nonactive player in turn order. (In a 1v1, that just means one opponent is the NAP.) The active player is whoever is currently having their turn.