There are two ways for a user to request a membership, and both have different ways to enable auto-approving a membership request.
Members can join your community in two ways:
Membership invite by link
Community sign up page
How to auto-approve membership requests when a user joins through membership invites:
When creating an invitation by email or by link, you can untick or tick this checkbox to enable auto-approval of membership request
Click this link for more information about membership invites
How to auto-approve membership request when a user joins through the community sign up page:
1. Click the Admin Panel button.
2. Click Settings on the side menu.
3. Click the General tab.
4. Tick the Automatically approve members checkbox to enable the auto-approved membership request when a user joins the community through the community sign-up page.
