Put new front signal bulbs in my daughters 02 Mazda Protege. When I signal left or right all of the lights flash as If the hazard lights are on. Is this wiring problem or could it be the wrong bulbs?

test the socket

Turn Signal Lamps
The body control module (BCM) is responsible for controlling the turn signals and hazard lamps. When the turn signal switch is placed in either the left turn or right turn position, the BCM receives a signal from the turn signal switch. The BCM then sends an on-off voltage signal to either the left or right turn signals and their instrument panel cluster (IPC) indicator. When the hazard switch is pressed, the BCM receives a signal from the hazard switch. The BCM then will send an on-off voltage signal to all the turn signal lamps. All the turn signal lamps will flash including both IPC turn signal indicators.
Stop Lamps
The body control module (BCM) is responsible for controlling the stop lamps. When the driver presses the brake pedal, the BCM will receive a signal from the brake pedal position sensor. The BCM then supplies battery positive voltage to both left and right stop lamp assemblies and to the center high mounted stop lamp (CHMSL). The stop lamps are grounded at G401 and G403. The CHMSL is grounded at G302.

Something is messing with the BCM'S mind ,bad input data ,shorted circuit etc... Hooking up a professional type scan tool is needed to read BCM DTC'S - diagnostic trouble codes an view live data to the BCM .

DTC B3948 02: Left Front Turn Signal Circuit Short to Ground
DTC B3948 05: Left Front Turn Signal Circuit Short to Battery or Open
DTC B3949 02: Right Front Turn Signal Circuit Short to Ground
DTC B3949 05: Right Front Turn Signal Circuit Short to Battery or Open

DTC B3950 02: Left Rear Turn Signal Circuit Short to Ground
DTC B3950 05: Left Rear Turn Signal Circuit Short to Battery or Open
DTC B3951 02: Right Rear Turn Signal Circuit Short to Ground
DTC B3951 05: Right Rear Turn Signal Circuit Short to Battery or Open

Your best bet ,take it to a qualified repair shop.

Get the left signal to flash fast then walk around the car to see which light isn't flashing then change the bulb or socket if they all appear to be flashing (front and rear) turn on the right turn signal then look into the front and rear lens and count the number of bulbs flashing, now do the same thing on the left. Many times there's more than 1 bulb in each lamp. I hope this helps. Take care.

Only the bulb is linked with those seperate items the bulb runs both blinker and hazard normally one goes both go when u have tufrn signal on inside if u hear it flashing fast its ur bulb

I don't believe it would be a bad ground for just one light. It could be a wire, a socket connector, or the bulb socket itself. See if the wire has power at the socket when signaling left, with key on. If there is power, probably a bad socket or connector. If no power, check for power coming from flasher-the wire going to front left, or driver's side. If you have power from the flasher, but nothing at the socket, the wire has probably broken.
Good luck.

Sounds like a short between the circuit for the 4-Ways and the multi-function switch (The lever that operates the turn signals). Have the system checked by a qualified mechanic.

That is a different filement in the bulb for the alarm. Try replacing all the outside bulbs.

make sure you have the correct replacement bulb for that car. Some bulbs do more than one thing.

Find the ground wire on one of the lights and add another ground wire to a good clean metal surface and see if that fixes the problem. It defently sounds like a ground problem at one of the lights.

Conrad, up north.
My protege is a '99. The turn signals and hazard flashers use the same flasher unit. It is located under the dash to the left of the steering wheel and above and a bit to the right right of the driver's side fuse box.