Here is a basic example of how to do this.

I also changed the logic a bit to update the values if the user changes them again. - @Ultimater mentioned this also.

function setupButton() {
  if (validEmail && validCheckbox) {
    // add/show/enable submit button or simply change the color
    button.style.color = "red";
  } else {
    // remove/hide/disable submit button revert the changes
    button.style.color = "";
  }
}
form.input.addEventListener('input', (event)=>{
  validEmail = emailRegex.test(event.target.value);
  setupButton();
})
form.checkbox.addEventListener('change', (event)=>{
  validCheckbox = event.target.checked;
  setupButton();
})

I would also suggest a different method to validate the form using the Constraint Validation API.

Every element has a validity check which can easily be accessed on the form element using formElement.checkValidity() and returns true/false if all (required) fields inside the form are filled with valid values.

<form oninput="this.querySelector('#submitButton').disabled = !this.checkValidity();" onsubmit="event.preventDefault(); console.log('Submit prevented but the form seems to be valid.'); return false;">
  <fieldset>
    <label for="newslettermail">E-Mail</label>
    <!-- you could also define a more specific pattern on the email input since email would allow foo@bar as valid mail -->
    <input type="email" id="newslettermail" required>
  </fieldset>
  <fieldset>
    <input type="checkbox" id="newsletterAcceptTos" required>
    <label for="newsletterAcceptTos">I accept the Terms of Service</label>
  </fieldset>
  <fieldset>
    <label for="textFieldWithPattern">Enter <strong>foo</strong> or <strong>bar</strong></label>
    <input type="text" id="textFieldWithPattern" pattern="^(foo|bar)$" required>
  </fieldset>
  <button type="submit" id="submitButton" disabled>Submit</button>
  <button type="submit">Force submit (will show errors on invalid input)</button>
</form>

Using this, the browser for itself checks the values if they contain a valid value.

• An input[type=email] with required flag must contain a valid mail address.
• A checkbox with required flag, must be checked.
• An input with required and a pattern must contain a value matching the regular expression from the pattern-attribute.

No need to create extra variables and listen on two form elements separately... You can check the whole thing and update accordingly only by listening to the form element

let form = document.querySelector('form');
let input = document.getElementById('input');
let checkbox = document.getElementById('checkbox');
let submit = document.getElementById('button');

const emailRegex = /^(([^<>()\[\]\\.,;:\s@"]+(\.[^<>()\[\]\\.,;:\s@"]+)*)|(".+"))@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}])|(([a-zA-Z\-0-9]+\.)+[a-zA-Z]{2,}))$/

form.addEventListener('change', (event) => {
  if (checkbox.checked && emailRegex.test(input.value)) {
    submit.style.color = "red";
  } else {
    submit.style.color = "black"
  }
})

//Update
input.addEventListener('input', () => {
  const changeEvent = new Event('change');
  form.dispatchEvent(changeEvent)
})

<form class="main__emailAndTerms emailAndTerms">
  <div class="emailAndTerms__email">
    <input type="text" id="input" placeholder="Type your email address here...">
    <label class="emailAndTerms__terms">I agree to <a href="#"><span class="terms__link">terms of service</span></a>
                <input type="checkbox" class="terms__checkbox" id="checkbox">
                <span class="terms__checkbox_custom"></span>
            </label>
    <button type="submit" class="email__submitButton" id="button">Submit</button>
  </div>
</form>