Illegal Screen?
 

I "no-called" a play which had everyone in an uproar.

A1 has an uncontested lay-up, going down the tableside sideline, then heads towards the basket on a 45-degree angle with the end line. A2 and B2 in motion, meet up at the tableside lane space closest to the FT line. A2 is between B2 and the basket. A2 and B2 both move at the same speed and same direction, from where they started, towards the basket. There is no contact, but they are only an inch apart.

It appears to all that A2 impeded B2's attempt to defend the play, as they moved together, step by step. But with no contact, no foul, correct?

Stand your ground ChuckS.
I've had the same type of play in games where I did not see contact but rather just syncrhonous motion between Ax and Bx who happened to be in very close proximity as Ay is engaged in a try for goal.
It's expected that the peanut gallery will rail against you; they don't have the well-positioned good "look/angle" on the play that you did.

You had Obstruction and you should have awarded Team B an Indirect Free Kick. Oops! Wrong sport, :p!

MTD, Sr.

Are there any fouls you can call that don't involve contact? What are those fouls and do they apply here?

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Rule 4-19-14 "An unsporting foul is a noncontact technical foul which consists of unfair, unethical, dishonorable conduct or any behavior not in accordance with the spirit of fair play".

To call this, I assume I would have to deem that A2 deliberately impeded B2, rather than just being in the wrong place at the wrong time?

In this instance, even if there was contact, I believe this is a case where a "moving screen" is legal. In fact, if B2 completely runs over A2, you might have a foul on B2.

4-40-6
When screening an opponent who is moving in the same path and direction as the screener, the player behind is responsible if contact is made because the player in front slows up or stops and the player behind overruns his/her opponent.

Personal fouls involve contact. Period.

(And no, technical fouls are not personal fouls.)

Even that wouldn't become an unsporting foul (or a T in HS). The rule is implying such acts as taunting, swearing, overly objecting to a call, etc.

Even if there is contact it doesn't mean the offense did anything wrong. They are entitled to their space on the floor and screening principles don't necessarily apply here.

???

If the defender is trying to get to the ball handler, why would they not apply?

In my case, A2 and B2 were not in the same path....but their paths were very close!

Regardless of the paths, if A2 does not come in contact with B2, there can be no foul because there would be no illegal contact.

So you are saying any moving offensive player is responsible for any contact made between said player and a defender?

Not any. But, if a defender is attempting to reach the ball handler, the offensive player's movements must be legal with respect to screening rules. If there is contact, the only direction they can be moving is directly away from that defender, otherwise, they've set an illegal screen.

I would disagree. This implies that an offensive player can only move "away" from any defender otherwise they are illegal. A player is entitled to their space and can move per the OP. Both players were moving parallel and "any" contact would not have been illegal for the offense.