In baseball can a player stand three feet from the plate in SWAT-like gear? Your team could have a line of players standing there and then a few fielders for the balls that get through and a first-basemen. What would be the ruling on a play like this?
This is covered in MLB rule 5.02:
5.02 (4.03) Fielding Positions
When the ball is put in play at the start of, or during a game, all fielders other than the catcher shall be on fair territory.
(a) The catcher shall station himself directly back of the plate. He may leave his position at any time to catch a pitch or make a play except that when the batter is being given an intentional base on balls, the catcher must stand with both feet within the lines of the catcher’s box until the ball leaves the pitcher’s hand. PENALTY: Balk.
(b) The pitcher, while in the act of delivering the ball to the batter, shall take his legal position;
(c) Except the pitcher and the catcher, any fielder may station himself anywhere in fair territory
There is no explicit prohibition in Rule 3 (equipment) to fielders wearing 'armor', though it does require uniforms with certain minimum standards (visible 6" number, for example) which may be challenging to accomplish while wearing armor.
It's unlikely this would ever work in practice, however, as the fielders would have to stand outside of the reach of the bat (else be called for batter interference); once they're out of the reach of the bat, the batter could undoubtedly hit the ball over their heads with ease. They'd also have to leave a wide enough area for the ball to get through on the pitch, which likely would be sufficient for a batter to regularly hit the ball through. Finally, they'd have to leave a lane for the batter to run in, and while the batter is primarily intended to run in foul territory to first, it seems likely that they'd have to leave some space right around the line (otherwise the batter would run into their arms).
And, of course, it's unlikely you'd manage to get sufficient armor on them to protect them from a ball travelling over 100mph off the bat while still permitting them to field the ball usefully.