Is there a way to force users to enter different email addresses for 2 different email input fields?

I have a reference check form, where we are asking applicants to provide the email addresses of 2 references that we can contact. 

Is there a way we can add/alter form validations so that the email address they enter in the Email1 field is required to be different than the email address they enter in the Email 2 field?   We want to prevent users from just entering their own email in each field.

You can do this by using a conditional logic and trigger a text field to show the error message. 

As a demonstration you can view my form https://form.jotform.com/82523963118964, try to enter the same email address in both email fields and it shows an error text and hides the Submit button.

You can do the following.
1. Created a hidden Text field to show an error message.
2. Create a Condition to Show the Text field and Hide Submit button if the value entered in Email1 & Email2 is equal.
Here is the screenshot of the condition.

Related article: Smart-Forms-Using-Conditional-Logic 

I hope this helps. Feel free to clone my form and get in touch if you have further questions.