How can I change a database value with a checkbox toggle using ajax?

You need to send some data in the AJAX request:

<script>
        $(function (){
            $('form.user-active .toggle').on('change', function (event) {
                $.ajax({
                type: 'POST',
                url: "{{route('user.profile.user-active')}}",
		data: {
			is_active: this.checked
		}
            });

            });
        });	
</script>

However, this is sending whenever the checkbox is changed; if you need to actually submit the form, then the event listener should be on the form submit event instead and the data to be send could simple serialize the jQuery object representing the form

@tykus - thanks for your reply. No the form doesn't need to be submitted - only when the checkbox is toggled. It's using submit at the moment though for the non ajax version, etc. I will give this a go

Ok, not that I didn't put the profile_id in the payload as well; it would be more appropriate to get this from the authenticated user in the controller instead (to prevent users toggling the is_active property for other users):

    public function changeUserActiveStatus(Request $request){

        $profile = auth()->user()->profile; 
	// assumes there is a `profile` relationship on the User model

        $profile->is_active = $request->is_active == 1 ? 0 : 1;

        $profile->save();

        return redirect()->back();
    }

@tykus I've taken care of that by passing the profile id in through $request->profile_id. Adding data: { is_active: this.checked } hasn't changed anything

In the end I found exactly what I was looking for with this like for like tutorial Laravel Update User Status Using Toggle Button Example I made it bespoke for what I needed and was able to add a flash style Bootstrap alert:

<script>
    $(function (){
        $('div.user-active .toggle').on('click', function (event) {

            var status = $('div.user-active .toggle input').prop('checked') == true ? 0 : 1; 
            
            $.ajax({
                type: "GET",
                dataType: "json",
                url: '{{route('user.profile.user-active')}}',
                data: {'is_active': status/*, 'user_id': user_id*/},
                success: function(data){
                    console.log(data.success);

                    var messages = $('.user-active-toggle-message');

                    var successHtml = 
                    '<div class="alert mb-0 mt-3 alert-success border rounded border-success">' + 
                        '<p class="mb-0"><i class="fas fa-check mr-2"></i>' + data.success  + '</p>' +
                    '</div>';

                    $(messages).html(successHtml).fadeIn().fadeOut(2500);

                }
            });


        });

    });
</script>

@tykus your answer didn't really help solve it but I'll give it to you as choosing my own is like giving myself a High 5 in public. I'm also using what you suggested for $profile = auth()->user()->profile; and this has meant I can just remove a hidden input and get rid of the form element altogether.