Is true that's not suitable to change the whole fluid of the transmission at once?

No, assuming your transmission was serviced properly -

• you drain everything with the drain plug (into bottles to measure amount),
• remove the oil pan,
• clean the magnets,
• replace ATF filter,
• install oil pan with RTV,
• remove the air filter box,
• refill through the dipstick hole (the same amount as came out),
• shift through all gears while sitting in the same place (with M1 and M2),
• wait until it heats to 50 degrees C,
• use the tiny dipstick to check level and if needed add more fluid,
• secure the dipstick in place requires the use of a bolt.

If you're not confident on how to do it, go to a mechanic that knows how to do it correctly on a Mazda.

But note that Mazda says it's "not recommended" https://static.nhtsa.gov/odi/tsbs/2022/MC-10208556-0001.pdf

I'd assume it's cause a lot of people end up doing it incorrectly and Mazda wants to sell new cars/transmissions.

Also OEM (ATF-FZ) fluid is blue, Mazda ATF fluid changes color (not only darkness) based on wear.

Check how it'll behave after the fluid change, if poorly reset the TCM.

I read online that on a Mazda it's done by "turn the key into Accessories mode, press the gas medal to the floor for at least 30 seconds." so maybe that'll work but usually you'd need a scan tool.

And should change a gallon at a time? 

A gallon is about as much as it'll come out, I think you meant a quart.

You replace a quart at a time if you're afraid that the transmission is too worn.

I am trying to avoid changing the whole transmission and maybe changing the fluid and the filter will fix it

Just an upfront disclaimer, if you've got to the point were it's misbehaving -

an oil and filter replaced may help it, but it also can make it worse.

I think it's worth a try, obviously at your own risk.