The general rule
Personal photography with phones and compact cameras is allowed at almost all NPB and J-League games. The restrictions are about how you shoot, not whether you can.
What's allowed
Smartphone photos and videos: yes. Compact digital cameras: yes. Mirrorless/DSLR cameras with standard lenses: usually yes, but check the specific stadium's policy. Short personal video clips: yes.
What's restricted
Flash photography
Prohibited during play at all stadiums. Flash can distract players, especially batters and goalkeepers. Turn off your flash before the game starts.
Tripods and monopods
Not allowed in seating areas. They block views and create tripping hazards in tight rows.
Selfie sticks
Banned at most stadiums. They obstruct views for people behind you.
Professional-grade telephoto lenses
Some stadiums restrict lenses over 300mm. If you're carrying a lens that looks like it belongs on a sideline, expect questions at the gate.
Video recording
Short personal clips are fine. Recording entire innings, halves, or significant portions of the game for redistribution is prohibited. Nobody will stop you from filming a home run or a goal for your Instagram story.