Updated January 19, 2020 

Yes. All new customers since September 2019 have access to Stripe Elements and Braintree Hosted Fields in their MemberMouse payment settings. These settings are enabled by default as of MemberMouse v2.4.0+ . So, unless deliberately unchecked, your checkout process will automatically comply with the Strong Customer Authentication (SCA) requirement. 

Read this post for more full information about SCA, MemberMouse and your site.

For MemberMouse customers prior to September 2019, an upgrade to MemberMouse version 2.3.0+ will be necessary to give you the tools to configure your checkout process to be in compliance.

In brief, the main requirement of PSD2 as relates to online businesses is Strong Customer Authentication (SCA) - similar to what people refer to as two-factor authentication - which necessitates a 3D Secure (3DS) checkout flow for initial and one-time purchases where both the initiating and acquiring banks are both in the European Economic Area (EEA). MemberMouse v2.3.0+ includes use of Stripe Elements and Braintree Hosted Fields in those payment provider configurations, both of which use 3D Secure 2.0 to secure transactions.