The movies can, but I have a feeling if one of the TV series wanted to do a plot that was similar to what they were planning on doing in one of the upcoming movies, they'd probably ask them not to do it. It's the same reason they used to do the character bans.
I find it hard to believe there isn't a lot of crossover between the shows and the movies. Yeah, a lot more people watch the movies than the shows, but I would be surprised if a lot of the people who watch the shows didn't also watch the movies.
The only real exceptions I could maybe see would be stuff that is a significant part of the character's backstory, for instance if we got a Wonder Woman show, I'm pretty sure we'd still start out with Diana growing up on Themyscira, and finding Steve Trevor once she's an adult. They'd probably set it in the modern day and give us a different villain from Ares though, so that would probably differentiate it quite a bit from the movie.
Well, DC did have the whole thing with Hal Jordan and the underage girl. There were also several other instances of them indicating Superman and Supergirl should hook up, I know at least one had a computer that was supposed to pick a person's perfect mate, and it picked Supergirl for Superman.