Wet carpet passenger side

Doors don't normally leak as they have seals all around the edge, and the glass, unless yours are missing . Do you have a sunroof in it? Drains block or the pipes come unattached.

https://www.mazda6club.com/threads/drivers-side-carpet-gets-wet-when-it-rains.189807/

Or you have a blocked drain in front of the windscreen.

Or you have a hole in the floor.

Or the AC Drain is blocked.

A simple test is to feel around the carpet in that footwell. See how far up under the dash the carpet is wet. Does it only happen after rain? Do you have a sun roof fitted?
If the carpet is only wet low down on the floor the most likely reason is either a perished or damaged door seal rubber, a faulty sun roof seal or the drain channels for the sun roof are clogged up. Check the footwell in the back as water always flows and settles at the lowest point in the vehicle.
If it is high up and nearest the middle of the dash you issue could be the heater matrix under the dash but as it seems to be only on one side this might not be the issue.
Door seals are a simple case of pull the old one off and push the new one on and they don't cost silly money to buy. Heater matrix issues, unfortunately, usually involve taking the whole dashboard out to get to it.
Hope this helps.

The two most common causes are rain water leaking in or the ac drain being clogged up. I would vote for rain water if the entire carpet area is wet.
Could be coming in around the windshield, or one of the door gaskets.

a couple things to look at if it has a sunroof the sun roof would have drain hoses that run down in each corner next you need to look at the cowl this is the section in front of the windshield that has a drain on it as well if you find nothing there the next step would be to remove the seats and carpet and sit in the car while running water over it either way you should remove the carpet and make sure it is dry all the way threw or mold will start to grow and you will never get ride of it not good for your heath other key spots to look at is if the windshield was ever replaced it could be a poor seal

does it have a sun roof and the drains are plugged up?

Could be several things:-

1) Pollen filter blocked, needs changing.

2) Sunroof drain blocked, my car is different but the sun roof drains down a tube which eventually goes down the rear of the front wing. There's one both sides. To clear, take the wheel off, take the inner wing shroud out and clean all the mud that has built up underneath it, Then make sure the tube is clean.

3) Faulty door seal, check your door frame seals.

check door/ boot seal on side that the carpet is wet .also if your car has a sun roof check the drain chanels.

If you've been using your air conditioner during this time, and it hasn't rained at all, then the small drain at the bottom of the a/c evaporator core may be plugged. When you use the a/c to cool the car the evaporator coil [located next to the heater core in the ductwork under the dash] is very cold and moisture from the hot humid air condenses on it as a result. This condensation dribbles down the core and accumulates in the plastic housing under it where it should then drain out a small hole and drip onto the ground. If the small drain gets plugged, which happens quite often, then the water fills up the housing until it overflows and then runs out and soaks the carpet on the front passenger side. The drain is located on the engine side of the firewall, passenger side, down low where the firewall begins to curve under. Usually a puff of air will clear the clog and the drain will work fine again. If the carpet is really wet it would be a good idea to remove it and get everything dry again as it tends to get pretty smelly if left wet. One last note: usually a leaky a/c unit will only make the passenger side carpet wet unless it's been leaking for a long time while a leaky windshield seal can make both sides wet depending on where it is leaking. Good luck, hope this helps you out!

Hi, we also have a 2002 Toyota Rav4 and developed a leak in the front driver's side of the car. After much research, we discovered that the drain wells from our sun/moon roof were clogged. If you have one of these, I suggest that you open the sun roof and look carefully. You will notice some tiny little holes in front and in the rear of the sun/moon roof tracks. Over time, these become clogged with dust and debris. You need to find a long, sturdy piece of thin wire and run it down the holes. To test if you have properly unclogged these, take a small amount of water and pour it down the holes. You should see water coming out of the drain wells under the car around the rear of the front tires. Hope this helps.

It sounds like a plugged drain line from the air conditioner. Most cars now run in the a/c mode whenever u turn on the climate control (even when heat is on). The passenger side front is where it would be wet, and the carpet and carpet pad act like a sponge and will soak up the water. Let me know how u make out.