An MX record is the DNS entry that routes email for a domain to whichever mail service handles it. It is entirely separate from the A or CNAME record that points the same domain at a website, so adding or changing a website record does not touch email, and changing email does not touch the website.
The one place the two can collide is changing nameservers rather than records: that hands the whole domain, including its MX records, to a new provider, and copying them across is the part people forget.
For the full picture of records, nameservers, and what breaks when, see connect a domain you already own.