My main comment is that you should separate the different concerns of you code into descriptive functions. This will make it a lot more readable (and re-usable).

One comment before I get started:
Your `login` function, which looks like it would log you in with the reddit API seems to be unused atm. I guess this is a copy&paste error from censoring?


----------

Your first concern is to log-in with gmail to get the `mail` object. This can be pasted directly into a separate function:

    def mail_login():
        mail = imaplib.IMAP4_SSL('imap.gmail.com')
        while True:
            try:
                emailpass = getpass.getpass(
                    'Please enter the password for xxxxxxx@xxxxx: ')
                mail.login('[email protected]', emailpass)
                break
            except imaplib.IMAP4.error:
                print('Incorrect password')
        mail.select("inbox")
        return mail

----------

The second task, which is repeated quite often, is to print a message with the current timestamp preceeding it:

    def log(text):
        print('\t{:%Y-%m-%d %H:%M:%S} - {}'.format(datetime.now(), text))

Note that I used the custom format options of `str.format` here.

----------

Another task is to post an alert to reddit, once it is found:
    
    def post_alert(alert, r):
        alert_text = """
        {}
    
         ********
    
         *^^I ^^am ^^a ^^bot. ^^For ^^any ^^questions, ^^comments, ^^or ^^concerns, ^^please ^^email [^^xxxxxxx@xxxxx](mailto://xxxxxxx@xxxxx)*
         """
        while True:
            try:
                r.submit(subreddit='xxxxxxxxxxxx', title=alert,
                         text=alert_text.format(alert))
                print('\t{}'.format(alert), end=' ')
                break
            except praw.errors.ExceptionList as e:
                log('Reddit error! {}'.format(e))
                time.sleep(300)


I build the alert text first and filled it with `str.format` and used the log function.


----------

The second to last task is to search in your emails for new messages and yield all alert texts:

    class ShortTimeOut(Exception):
        pass

    def search_for_alerts(mail):
        result, response = mail.uid('search', None, "(UNSEEN)")
        unread_msg_nums = response[0].split()
    
        result, data = mail.uid('search', None, "ALL")
        latest_email_uid = data[0].split()[-1]
        result, data = mail.uid('fetch', latest_email_uid, '(RFC822)')
        raw_email = data[0][1]
    
        email_message = email.message_from_bytes(raw_email)
    
        if unread_msg_nums:
            log('Something\'s wrong!')
            for part in email_message.walk():
                if part.get_content_type() == 'text/plain':
                    yield part.get_payload()
        else:
            raise ShortTimeOut

I did not change a lot here, except that I yield the email contents (to be iterated over in the outer scope). I also added a custom exception to allow handling the short timeout in `main`.


----------

The last function is a main function, which calls all the other functions. It is executed in a `if __name__ == "__main__":` guard to allow importing your code from other scripts:

    def main():
        while True:
            try:
                r = RUAlerts.login()
                mail = mail_login()
                try:
                    for alert in search_for_alerts(mail):
                        post_alert(alert, r)
                except ShortTimeOut:
                    log('All clear on the RU front')
                    time.sleep(30)
    
            except Exception as e:
                log('{} Retrying in 5 minutes'.format(e))
                time.sleep(300)
    
    
    if __name__ == "__main__":
        main()

----------


**Final code:**

    import praw
    import imaplib
    import email
    import time
    import getpass
    import RUAlerts
    from datetime import datetime

    class ShortTimeOut(Exception):
        pass
    
    app_id = 'xxxxxxxxxxxx'
    app_secret = 'xxxxxxxxxxxx'
    app_uri = 'xxxxxxxxxxxx'
    app_scopes = 'account creddits edit flair history identity mysubreddits privatemessages read report save submit subscribe vote'
    app_ua = 'xxxxxxxxxxxx'
    app_account_code = 'xxxxxxxxxxxx'
    app_refresh = 'xxxxxxxxxxxx'
    
    
    def login():
        r = praw.Reddit(app_ua)
        r.set_oauth_app_info(app_id, app_secret, app_uri)
        r.refresh_access_information(app_refresh)
        return r
    
    
    def log(text):
        print('\t{:%Y-%m-%d %H:%M:%S} - {}'.format(datetime.now(), text))
    
    
    def mail_login():
        mail = imaplib.IMAP4_SSL('imap.gmail.com')
        while True:
            try:
                emailpass = getpass.getpass(
                    'Please enter the password for xxxxxxx@xxxxx: ')
                mail.login('[email protected]', emailpass)
                break
            except imaplib.IMAP4.error:
                print('Incorrect password')
        mail.select("inbox")
        return mail
    
    
    def post_alert(alert, r):
        alert_text = """
        {}
    
         ********
    
         *^^I ^^am ^^a ^^bot. ^^For ^^any ^^questions, ^^comments, ^^or ^^concerns, ^^please ^^email [^^xxxxxxx@xxxxx](mailto://xxxxxxx@xxxxx)*
         """
        while True:
            try:
                r.submit(subreddit='xxxxxxxxxxxx', title=alert,
                         text=alert_text.format(alert))
                print('\t{}'.format(alert), end=' ')
                break
            except praw.errors.ExceptionList as e:
                log('Reddit error! {}'.format(e))
                time.sleep(300)
    
    
    def search_for_alerts(mail):
        result, response = mail.uid('search', None, "(UNSEEN)")
        unread_msg_nums = response[0].split()
    
        result, data = mail.uid('search', None, "ALL")
        latest_email_uid = data[0].split()[-1]
        result, data = mail.uid('fetch', latest_email_uid, '(RFC822)')
        raw_email = data[0][1]
    
        email_message = email.message_from_bytes(raw_email)
    
        if unread_msg_nums:
            log('Something\'s wrong!')
            for part in email_message.walk():
                if part.get_content_type() == 'text/plain':
                    yield part.get_payload()
        else:
            raise ShortTimeOut
    
    def main():
        while True:
            try:
                r = RUAlerts.login()
                mail = mail_login()
                try:
                    for alert in search_for_alerts(mail):
                        post_alert(alert, r)
                except ShortTimeOut:
                    log('All clear on the RU front')
                    time.sleep(30)
        
            except Exception as e:
                log("{}! Retrying in 5 minutes".format(e))
                time.sleep(300)

    if __name__ == "__main__":
        main()