Add this CSS to any page that might display the profile modal.

<style>
.ms-portal-content label[for="email"]{
z-index: -1;
cursor: not-allowed;
position: relative;
}
.ms-portal-content label[for="email"]::after{
content:" (Please contact us)";
}
.ms-portal-content [data-cy="emailField"]{
z-index: -2;
opacity: 60%;
cursor: not-allowed;
position: relative;
}
.ms-portal-content [ms-lang="email_update"]{
display: none;
visibility: hidden;
}
</style>
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