For commercial items:
Pretty much, if you’re not selling or giving away your modified textures you’re fine. You CAN sell renders or animations.
Many freebies come with a “non-commercial use” or “contact me first” statement. This is usually because someone else own the rights to the character, etc. This wouldn’t prevent you from doing what you asked about, but you would have to keep track of the modified product an non-commercial etc.
To summarize: You can probably do this and avoid any trouble as long as you follow the rules for the original stuff.