Hey @sperrier,
When the PayPal button is clicked, I am directed to PayPal to complete the membership checkout, but as this is a plus add-on, the moderators of this forum require that all inquiries about paid products happen elsewhere, so I would suggest reaching out to the Paid Memberships Pro member support team for guidance debugging your issue.
@sperrier this appears to be an issue with mixed-content and possibly your theme.
Can you go to Appearance->Themes. Select a WordPress default theme. Instead of activating it, go to Live Preview. From there, navigate to your checkout page and see if the problem is still there.
Also, double-check your payment gateway settings. You shouldn’t require a third-party add on for this. PayPal is built-in.
Regards,
Ronald Huereca