Preventing auto-filling of e-mail addresses on profile.php

You can try to inject an autocomplete attribute into the form element on that page. There is a dedicated action for that: user_edit_form_tag.

add_action( 'user_edit_form_tag', function() {
    print ' autocomplete="off"';
});

If that doesn’t help – and it looks like the new IE has a bug here – you could try the solution from this Stack Overflow answer.

Here is some untested(!) code. jQuery is always available on the page, so we don’t have to take care of that. Note that I nested the callback registrations, because the constant IS_PROFILE_PAGE is only defined when the action user_edit_form_tag has been actually called.

add_action( 'user_edit_form_tag', function() {
    print ' autocomplete="off"';

    // See https://stackoverflow.com/questions/22817801/how-to-disable-auto-fill-in-safari-7
    $extra_action = IS_PROFILE_PAGE ? 'show_user_profile' : 'edit_user_profile';

    add_action( $extra_action, function() {
        ?>
<style>
.douchebag_safari {
    position: fixed;
    width: 1px;
    left: -5000px;
}
.douchebag_safari input {
    width: 1%;
}
</style>
<div class="douchebag_safari">
    <input class="js-clear_field" tabindex="-1" name="e-mail" type="email">
    <input class="js-clear_field" tabindex="-1" name="Ecom_User_Password" type="password">
</div>
        <?php

        add_action( 'admin_print_footer_scripts', function() {
            ?>
<script>
    jQuery('#your-profile').on('submit', function () {
        "use strict";
        jQuery('.js-clear_field').attr('disabled', 'disabled');
    }
</script>
            <?php

        });
    });
});