You can create a RegExp from filterstrings first

var filterstrings = ['firststring','secondstring','thirdstring'];
var regex = new RegExp( filterstrings.join( "|" ), "i");

then test if the passedinstring is there

var isAvailable = regex.test( passedinstring );

Here is a test implementation:

// Take care to escape these strings!
// If they are user-input or may contain special regex characters (such as "$" or "."), they have to be escaped.
var filterStrings = ['one','two','three'];
var regex = new RegExp(filterStrings.join( "|" ), "i");

var sentences = [
  "one", // true
  "OnE", // true
  "a rabbit", // false
  "and then two rabbits", // true
  "standing", // false
  "prone", // true
  "AoNeAtWo", // true
];
sentences.forEach(sentence => {
  console.log(
    regex.test(sentence) ? ' match:' : ' not a match:',
    "'" + sentence + "'",
    );
});

Add .toUpperCase() after referrer. This method turns the string into an upper case string. Then, use .indexOf() using RAL instead of Ral.

if (referrer.toUpperCase().indexOf("RAL") === -1) { 

The same can also be achieved using a Regular Expression (especially useful when you want to test against dynamic patterns):

if (!/Ral/i.test(referrer)) {
   //    ^i = Ignore case flag for RegExp

ES2015 findIndex:

var array = ['I', 'hAve', 'theSe', 'ITEMs'],
    indexOf = (arr, q) => arr.findIndex(item => q.toLowerCase() === item.toLowerCase());

console.log(  indexOf(array, 'i')      ) // 0
console.log(  indexOf(array, 'these')  ) // 2
console.log(  indexOf(array, 'items')  ) // 3

I would suggest using a Map instead of an array for your todo list. A Map has the advantage that it provides key-based look-up in constant time, and does not store duplicate entries with the same key. You could then use the lower case variant as the key, and the original (mixed-case) string as the value for that key.

You could define todos as a Map instead of an array, and use the lower case string as the key:

constructor(props) {
    super(props);
    this.todos = new Map();
    this.addToDo('Get Up from bed'); 
    this.addToDo('Eat Breakfast');
}

Then, to add the task becomes very straightforward, as a Map overwrites duplicates:

addToDo() {
    this.todos.set(task_title.toLowerCase(), task_title);
    this.setState({
        todos: this.todos
    });
 }

In rendering you would need to use Array.from(..., <map-function>), as .map is not defined for Map objects:

<div className="todos">
    {Array.from(this.todos, this.eachTodo)}
</div>

Which means the eachToDo method will receive a pair of strings (an array), instead of a string, and we want to display the second of the pair, so using index [1]:

eachTodo(task, i) {
    return (
        <Todo key={i} index={i}>{task[1]}</Todo>
    )
}