If they sent the email to Grard's personal email and he responded from his personal email, the firing violates the 1st Amendment and he can sue.
But if he received it via the company email system, forwarded it to his email, and responded from his personal email, but with his company email still displayed, that might violate company policy (since he would appear to be speaking for the company).
Sorry, you're wrong. Private political opinions are protected from government retaliation, not from employer retaliation.
Pseudonyms are our friends. I hate to think how many jobs I won't be qualified for just because I've voiced controversial opinions under my real name.
Of course, if employers think defending marriage is controversial, perhaps they don't deserve my labor anyway.