Is it ok to have people agree use an 'anti-cheat software' for computer games legal?
Sure. That sounds OK. You have to agree if you want to play so there is no coercion. Don't want to do it, then don't play. Pretty simple.
But is there a limit on what they can scan for and where?
That is a little harder to answer. They are making the software so they can make it do whatever they want. They have an interest in wanting people to play so they have some incentive to not scan for things they shouldn't need to. If someone finds out their scanner is doing things it shouldn't then people won't play. Of course, if you play and the scanner invades your computer and steals information, it will be too late for you. The flip side is if people know what the scanner is looking for they can hide it from the scanner and still be able to cheat.
So, that only raises more questions for you than it answers.
1. Do you trust the people that are scanning your computer?
2. Even if you trust them, is there a way to double check what they are sending.
3. Are you willing to risk the invasion to play the game?