Of course the spell won't resolve, but is the indestructible creature a legal target for a spell with the effect "destroy target creature"?
Yes, Indestructible creatures are legal targets for spells/abilities that say "destroy target creature."
The spell actually does resolve, but when it attempts to destroy the creature rule 700.4 prevents it from happening. The requirements for a "legal target" for a spell must be a permanent, unless the spell/ability specifies otherwise. Indestructibility does not modify the rules for targeting, unlike the rules for protection (702.15b A permanent or player with protection can’t be targeted by spells with the stated quality and can’t be targeted by abilities from a source with the stated quality).
You can target Gideon with Rapid Hybridization, and when it resolves it will fail to destroy Gideon and will create 3/3 frog owned by Gideon's controller.
114.2. Only permanents are legal targets for spells and abilities, unless a spell or ability (a) specifies that it can target an object in another zone or a player, (b) targets an object that can’t exist on the battlefield, such as a spell or ability, or (c) targets a zone.
700.4. If a permanent is indestructible, rules and effects can’t destroy it. (See rule 701.6, “Destroy.”) Such permanents are not destroyed by lethal damage, and they ignore the lethal-damage state-based action (see rule 704.5g). Rules or effects may cause an indestructible permanent to be sacrificed, put into a graveyard, or exiled.
You can target anything that matches the description given for what's a legal target (unless Shroud, Hexproof or similar prevents you). Rapid Hybridization has you pick a target creature. Since Gideon, Champion of Justice is a creature (at this time), you can pick it as the target.
But Gideon is indestructible (at this time). It can't be destroyed [CR 700.4], but Rapid Hybridization instructs you to destroy it. Can't trumps do [CR 101.2], so you're asked to do something impossible.
609.3. If an effect attempts to do something impossible, it does only as much as possible.
So in this case, the following happens:
Destroy target creature. It can't be regenerated.That creature's controller puts a 3/3 green Frog Lizard creature token onto the battlefield.
Gideon's controller will get to keep Gideon, and he will gain a Frog Lizard.