In addition to the SPF/DKIM and DMRC reply above (which is a great place to start), check to see what email address the email is being sent from. More and more hosts are modifying their outgoing mail servers to force any form driven emails to change the sender email address to the server's hostname (such as firstname.lastname@example.org).
Another thing you can also do to help smooth things out is to plug in an actual SMTP user account. For this, you'll need to use a plugin like WP Mail SMTP or the gMail SMTP plugin. Follow the directions from whichever plugin you install.
Also, you might want to whitelist the email address the contact form emails are originating from within your gmail account.
To whitelist an email address in Gmail, sign in to your account at Gmail.com and do the following.
- Add the address to your contacts
Add the email address that is sending you email (eg email@example.com) to your Gmail Contacts. Google will usually deliver email from addresses that are in your Contacts.
- Mark messages as ‘Not spam’
If Gmail has marked emails you wish to whitelist as spam, tell Gmail the emails are not spam.
- In Gmail, navigate to the spam folder.
- Search for emails containing the domain you wish to whitelist (eg onlinegroups.net).
- Select the emails that are not spam.
- Click More and then Not spam.