Updated November 17, 2020
Yes. All new customers since September 2019 have access to Stripe Elements and Braintree Hosted Fields in their MemberMouse payment settings. Activating this setting configures your checkout process to comply with the Strong Customer Authentication (SCA) requirement.
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.