Our umpires always ask at the plate meeting if all of our players are properly equipment according to the rules of Little League to play in the game. As a manager I always say absolutely, because I ask/check before every game.
I remember a game where the opposing Manager was a female and said "I don't know". She then said she was not going to ask a bunch of boys what they were wearing under their uniforms. Well that delayed the start of the game by a little bit while the Umpire went to the dugout to talk to the players and her male coaches.
As for bats, helmets, catchers gear, it needs to be checked. I am personally known for pulling my players gear from the dugout if they are not allowed to use it.
I coached a Junior team last year where the opposing team was using illegal composite bats that did not meet the Juniors rule. My Manager was not questioning it because the league was "not checking bats this year". A player came to me and asked if he could use his "illegal" travel ball bat. I just looked at him and said, "make your own decision". I did not watch what he took to the plate. First pitch, strike. Second pitch, 320 foot home run. As he came in he showed me his LEGAL bat. I told him I was extremely proud of him for the bat selection. Oh I also told him good first time Juniors homerun, by the way. Just trying to build a better human being!