Implementing console.table in JavaScript
Here are some things that can be improved


Naming: 


toTable is expressive but also confusing. It looks like it is converting something to table. When used in conjunction with HTML this could be confused with &lt;table&gt;. Adding comments to the function can be helpful to understand what the function is doing. But again, if comments are needed that means you're not naming variables correctly.
obj the short of object is descriptive when used for naming object. However, for this function it is wrong as the function is expecting an array. arr or array would be better.
arr Again, the variable is used to store a string. str can be used or some developers even use str as prefix e.g. strTable, strLine.



Repetitive Code:


'--------------------------\r\n' is used three times in the code. You can create a variable to store this string value and use it anywhere to add the line of hyphens.


for loops:

for loops is used three times in the code. Nested loops should be avoided. There are very few cases when nested loops are required. Always try to avoid nested loops wherever possible.

In the first loop, the keys of the object are joined using tab character.

for (let [key, value] of Object.entries(obj[0])) {
    arr += ' ' + key + '\t';
}


This can be done using Object.keys() which returns an array of keys. Then Array#join can be used on keys array to join the array elements by glue-\t in this case.

So, the new code will be

Object.keys(arr[0]).join('\t') // That's it!


The other nested loop will be slow if object is having large number of properties. 

for (let i = 0; i &lt; obj.length; i++) {
    arr += '\r\n--------------------------\r\n';
    for (let [key, value] of Object.entries(obj[i])) {
        arr += ' ' + value + '\t\t';
    }
}


Looking at it carefully shows that this only create a string of values separated by tab. Object.values can be used for this. But again, as the objects are inside array, it need to be iterated over and then values can be extracted from object. New code using this function will look like

arr.forEach(function(obj) {
    someVar += line + Object.values(obj).join('\t\t'); // Sweet!
});




Apart from these, below are some suggestions:


Using console.table consistently: If console.table is supported by target environment then why not use the beautiful function? Although, this function(toTable() from question) is not complete as it doesn't support printing object in table, object containing different keys, nested object, etc. For the basic implementation, it can override default method.

if (!console.table) {
    // Use fallback only when not available
    console.table = function(arr) {
        // Code here
    };
}

Creating the horizontal line dynamically.

The horizontal line is static. In case when the object contain less/more properties, it'll not fit correctly. To create the line dynamically again, Object.keys() can be used.

'-'.repeat(8 * keys.length) // Assuming a tab(\t) is eight characters long

Using monospace font to log data

For non-monospace fonts not all characters occupy same space. For example, i takes less space than O. console.log can be set with custom font using the second parameter which is CSS styles.

console.log('%c' + someString, 'font-family: monospace');



Here's code with these changes

if (!console.table) {
    console.table = function(arr) {
        'use strict';

        let keys = Object.keys(arr[0]);
        const horizontalLine = '\r\n' + '-'.repeat(8 * keys.length) + '\r\n';
        let heading = Object.keys(arr[0]).join('\t');

        let str = horizontalLine;
        str += heading;

        arr.forEach(function(obj) {
            str += horizontalLine + Object.values(obj).join('\t\t');
        });
        str += horizontalLine;
        console.log('%c' + str, 'font-family: monospace');
    };
}

let arr = [
    { firstName: 'Sirwan', lastName: 'Afifi', age: 27 },
    { firstName: 'Person2', lastName: 'P2', age: 32 }
];
console.table(arr);


Here's fiddle to try out it.

And here's output of the above code

------------------------
firstName   lastName    age
------------------------
Sirwan      Afifi       27
------------------------
Person2     P2      32
------------------------


Note:


As some of the features are only available in latest browsers/nodeJS version and some are experimental, see the MDN link embedded for browser support and polyfill.
This, by any means is not polyfill for console.table. This is just another version of the OP's code. console.table is overriden with assumptions that only the provided input format is used to log in table.
The horizontal lines are not perfect. They can contain less/more depending on the min and max length of key in the object.