JSFiddle - React, Tailwind, and code Playground

HTML

<select>
    <option></option>
    <option class="bob1">bob</option>
    <option class="bill2">bill</option>
    <option class="steve3">steve</option>
</select>
<select>
    <option></option>
    <option class="bob1">bob</option>
    <option class="bill2">bill</option>
    <option class="steve3">steve</option>
</select>
<select>
    <option></option>
    <option class="bob1">bob</option>
    <option class="bill2">bill</option>
    <option class="steve3">steve</option>
</select>
<select>
    <option></option>
    <option class="bob1">bob</option>
    <option class="bill2">bill</option>
    <option class="steve3">steve</option>
</select>

JavaScript

$(function() {
    $("select").on("change", function() {
        //reset to showing all the options
        $("select option").show(); 
    
        //for each selected option
        $("select option:selected").each(function() {
            var optionSelected = this;
            var playerID = $(this).attr("class");
            //hide the option in all the other dropdowns
            $("option." + playerID).each(function() {
                if(this != optionSelected) {
                    $(this).hide();
                }
            });
        });
    });
});