I have a one handle shower/tub faucet, and when you run straight hot water (to preheat for example) the water shuts itself off. Lever is still in the lifted/on position however. Cold is fine, even warm will keep running, problem is only with straight hot. Any ideas?

Hot on left.
Cold on right.
Some single handle faucets have bleed-over where both hot and cold enter mixing valve each time handle is turned on, even when faucet calls for just cold or just hot.
Otherwise maybe a do-it-yourself plumber got pipes backwards... or maybe the tub used to be on other side of wall, and tub was moved during remodeling but pipes were not changed.

To fix problem:
First of all, turn off shower faucet. Turn on Hot at sink and put ear against shower faucet listening for sound of water flowing through the mixing valve.
If mixing valve is working fine, you need to open wall and investigate more.
For example if you have access door, reach in and feel which pipe is hot.
Pipes might need to be reversed if problem comes up in home inspection, otherwise the problem will not harm anything.

If I understand correctly, you have single handled shower faucet.
Normally there is a wait for hot water to arrive at faucet.
But now hot water is already at shower faucet.

Single handled faucets have a mixing area inside valve where hot and cold come together before going into sink.
This mixing valve can have crossover where the hot and cold can pass through to each other even when faucet handle is off. When single handle faucets get old, this can happen.
How it happens:
For example another faucet is turned on inside house, and pressure differential between hot and cold causes hot water at shower handle to pass through mixing area and into cold water line.
So if another faucet has been run, then that lets hot flow to faulty single handled shower faucet.
To confirm this is the problem: turn on other faucet and put ear against shower faucet to listen for moving water.
This condition may also signal there is a water leak.
The problem is not harmful, but will draw cold water into water heater each time, and is energy wasteful.
Replace faucet or have plumber repair problem.

Replace valve canister- no construction- just remove after taking time to shut off water- a few screws and the job takes 15 minutes. I take for granted you have good water hot/cold to the fixture. This fix will cure most temperature balance problems.
The single lever system is a EZ care system. Note the canister can malfunction faster when exposed to untreated hard water.

do you have hot water elsewhere? if not, might be that your water heater is not heating.
if you do have hot water elsewhere, did you let the faucet run for a minute or 2.
did you have hot water before? is this a new house? new valve?
need a little more detail.
on posi temp valves, if there were no water coming out of the hot side of the valve, the valve will not operate.

these valves can be adjusted by removing the handle and adjusting the white gear that regulates the hot and cold that come out, try going more to one way if it gets colder then go the other way.

You can cap the lines at the tub faucet to rule out tub faucet. It maybe mixing there.

Faucet may be bad also the safety stop will alow you to change water temp it can be tricky to adjust water temp.

shut water off at stops under sink. Unscrew water supply lines from directly below handles. Above them you will find plastic nuts, remove them. Disconnect pop/up lever and you should be able to lift faucet from sink.

The only possible explaination is that the water is finding it easier to go up than down. Water is lazy, just like me. ;)

Use an allen key to remove the tub spout. It's underneath and awkward. Once the allen key is loose, the spout just slides off. Try running the water. This may solve your problem and all you'll need is a new tub spout. If not.....

Turn the water off to the house.

Use an allen key to remove the handle.

Use a phillips to remove the trim plate (2 screws). Cut the silicone around the trim if it's there (which, in a proper installation it shouldn't be, but...)

Unscrew the nut (usually chrome) holding the cartridge into the brass body of the valve. The cartridge pulls straight out. Check for restriction in the ports of the cartridge itself. Check for restriction in the line going down to the tub spout. If you can't find anything, replace the cartridge.

Reassemble & Enjoy!

Did the hot water shut off get turned back on fully after the change? Is the hot water line kinked under the sink? Is the hot water shut off valve working?

If you need further help, I’m available over the phone at https://www.6ya.com/expert/craig_3fa289bf857b1a3c

are the handle extensions on the cartridges all the way. i know sometimes the moens are a pain after you put the trim on to get them on and seated right so it actually spins the cartridge. also check the cartridge alignment the cartridges have little white tabs on the sides that correspond with a slot in the valve body if they aren't aligned it won't shut off either