Can only offer my own opinion, but:
Sports: Same logic which was used for banning trans women from playing women in chess can be used for any other sport. Won't get into the details of what that logic is unless asked to.
Awards: If it's a female only competition, then fair, but it's up for the organisation which hands the awards.
Digital art is a medium where trans women are often supported. If there is a female only art competition, for some reason, and the organisers are okay with trans women participating, then I think they should and be able win whatever award there is.
Most artists will be supportive.
Groups: If everyone in a group is okay with it, then they can be included.
When it comes to private groups and independent organizations, women possess the agency to decide who they welcome into their own spaces.