The rule
A professional team's name, logo, and uniform design, and a league's marks, belong to those organizations. Snapshot's terms of service list creating cards with copyrighted sports team logos without permission among the things users may not do, and the logo upload in the builder asks you to acknowledge that you have the right to use what you upload.
What is fine
Your youth club, school, or rec league logo, used with that organization's okay, is the ordinary use. A photo of a player wearing their own uniform is a photo of them; the card celebrates the player, not the mark. Partner organizations get templates carrying their own branding by design.
What the templates are
Snapshot's templates are original designs. They are not licensed reproductions of any card manufacturer's products or any league's branding, and a card made here is a personal keepsake rather than an official product of any team or league.
If you are unsure
Ask the organization that owns the mark. For a school or club that is usually a quick yes. For a professional team or league, assume no unless you have a written license.
