Uncaught Invariant Violation: Too many re-renders. React limits the number of renders to prevent an infinite loop

I suspect that the problem lies in the fact that you are calling your state setter immediately inside the function component body, which forces React to re-invoke your function again, with the same props, which ends up calling the state setter again, which triggers React to call your function again.... and so on.

const SingInContainer = ({ message, variant}) => {
    const [open, setSnackBarState] = useState(false);
    const handleClose = (reason) => {
        if (reason === 'clickaway') {
          return;
        }
        setSnackBarState(false)

      };

    if (variant) {
        setSnackBarState(true); // HERE BE DRAGONS
    }
    return (
        <div>
        <SnackBar
            open={open}
            handleClose={handleClose}
            variant={variant}
            message={message}
            />
        <SignInForm/>
        </div>
    )
}

Instead, I recommend you just conditionally set the default value for the state property using a ternary, so you end up with:

const SingInContainer = ({ message, variant}) => {
    const [open, setSnackBarState] = useState(variant ? true : false); 
                                  // or useState(!!variant); 
                                  // or useState(Boolean(variant));
    const handleClose = (reason) => {
        if (reason === 'clickaway') {
          return;
        }
        setSnackBarState(false)

      };

    return (
        <div>
        <SnackBar
            open={open}
            handleClose={handleClose}
            variant={variant}
            message={message}
            />
        <SignInForm/>
        </div>
    )
}

Comprehensive Demo

See this CodeSandbox.io demo for a comprehensive demo of it working, plus the broken component you had, and you can toggle between the two.

In SnackbarContentWrapper you need to change

<IconButton
          key="close"
          aria-label="Close"
          color="inherit"
          className={classes.close}
          onClick={onClose}
        >

to

<IconButton
          key="close"
          aria-label="Close"
          color="inherit"
          className={classes.close}
          onClick={() => onClose}
        >

so that it only fires the action when you click.

Instead, you could just curry the handleClose in SingInContainer to

const handleClose = () => (reason) => {
        if (reason === 'clickaway') {
          return;
        }
        setSnackBarState(false)

      };

It's the same.

You must link an event in your onClick. Additionally, the click function must receive the event. See the example

export default function Component(props) {

    function clickEvent (event, variable){
        console.log(variable);
    }

    return (
        <div>
            <IconButton
                key="close"
                aria-label="Close"
                color="inherit"
                onClick={e => clickEvent(e, 10)}
            >
        </div>
    )
}