DAX Optimization Help Needed - Measure That Calculates On Each Date Point in a Line Chart

You could try creating a summary table which pre-calculates the rate for a given day.

Dynamic Retention Rate Table =
ADDCOLUMNS (
    CALENDAR ( DATE ( 2024, 1, 1 ), DATE ( 2024, 12, 31 ) ),
    "Retention rate",
        VAR SelectedDate = [Date]
        VAR SelectedDateMinus367 = SelectedDate - 367
        VAR CurrentMembers =
            CALCULATETABLE (
                DISTINCT ( 'Invoice'[membership__c] ),
                ALL ( 'Invoice' ),
                'Invoice'[CreatedDate] <= SelectedDate,
                'Invoice'[Expiration_Date__c] >= SelectedDate,
                'Invoice'[Membership_Type__c] <> "Trial Membership"
            )
        VAR Members367DaysAgo =
            CALCULATETABLE (
                DISTINCT ( 'Invoice'[membership__c] ),
                'Invoice'[CreatedDate] <= SelectedDateMinus367,
                'Invoice'[Expiration_Date__c] >= SelectedDateMinus367
            )
        VAR ActiveBoth =
            INTERSECT ( CurrentMembers, Members367DaysAgo )
        VAR CountActiveBoth =
            COUNTROWS ( ActiveBoth )
        VAR CountMembers367DaysAgo =
            COUNTROWS ( Members367DaysAgo )
        RETURN
            DIVIDE ( CountActiveBoth, CountMembers367DaysAgo )
)

It would take a while to create the table during data refresh, but that would be invisible to end users.