Rex first: For the brief time that the Tide was in the wash water, it did not damage the aluminum tub but, of course, you had to rinse it out, just as you had to rinse the wringer rollers with running water. When I rinse the wringer washer, I can't resist playing in the water so I start the agitation and let the hose start filling the tub. After an inch or two of water get in the machine, that slow stroke Gyrator slaps it so hard, it sends it flying. It almost resembles a dishwasher on Qualude, maybe. Actually the aluminum tub was no worse with Tide than with the very strong washing soda and lye soap that was used before detergents. One CU article shows an early Maytag wringer washer that had a tall post drive and the damage to the aluminum if the strong wash solution sat in the tub overnight. It looked like something Lilo and Stitch attacked.
Georgio next:
The agitator just lifted out with an upward tug if you kept everything clean, dry and greased. You actually greased the splines at the top of the transmission shaft and that transferred the coating to the ones inside the base of the agitator. People who used these machines followed these directions. Maytags were very expensive washers. Most people who had them, or even early automatics, had lived through the Great Depression and knew the value of everything. Use it up, wear it out, make it do or do without. Wasteful ways make woeful wants. Most people buying a wringer washer had used tubs and scrub boards to wash clothes. Clothes were put in a strong soap solution to soak overnight. That was drained and the sink or tub was filled with hot water, which usually had to be heated in those old copper, if you had money, or tinned steel if you didn't, boilers on a stove. My Father's mother had, in her basement just across from the washer, a kerosene stove with 3 burners in a row across the front for the boiler. The big , clear reservoir of kerosene was pretty neat. So when doing all of this by hand, you scrubbed dirty places with soap and the washboard and plunged each piece up and down in the soapy wash water. Then you either twisted things to wring out by hand, or used a hand-cranked wringer that was bolted between sinks if you were lucky enough to have them. Think about doing all of the sheets by hand. Oh yeah, the old laundry sinks were low and deep, so you were bent over this hot soapy water most of the time. If you were washing diapers or other white things, they might be put on to boil while you washed everything else so that all of the soap would dissolve and rinse free of the fabric because if it stayed, it irritated and in things that were ironed, remaining soap caused an ugly brown stain when hit with a hot iron. So if you were lucky enough to have a machine that agitated the laundry for you and provided a powered wringer, you knew that you were damn lucky and took care of it. Maytag's Belly Button was not the power switch. You plugged the machine into an outlet and the motor ran. You quickly pulled the belly button out to engage the transmission and it could make some horrible noises if pulled out slowly or not fully engaged. The reason the machines had to be taken apart and rinsed was that it was the only way to rinse the strong cleaning agents from all parts of the machines and to make sure, when you were washing with soap, that you got all of the curd and goo rinsed off all of the parts. If you had a drain pump, you had to take the agitator out to clean the porcelain strainer/pump guard. Automatics did not need this so much because rinsing was done in the same tub. That's why it states in so many early automatic washer ads that, "It washes, rinses, spins dry, cleans itself and shuts off, all automatically." If the wringer rollers were not rinsed and /or the tension not released, the rollers could stick together and that might lead to tearing of the covering and money spent on repair, woe, woe, etc.
Jaune, when a friend got a new Hotpoint washer in the early 60s, the man who delivered it told her that Tide would eat it up, so if she wanted it to last, use something else. Mom always rinsed everything twice and it must have prevented corrosion from the lingering alkalinity because service people told her our washer looked like new inside compared with others they worked on.