Kulrath Knight has an effect that states 'Creatures your opponents control with counters on them can't attack or block.' So a creature is assigned as an attacker and subsequently gets a counter placed on it prior to combat resolution, does that remove the creature from combat?
No, making a creature "unable to attack or block" after attackers have been declared does not remove it from combat.
An ability that says "Creatures can't Attack or Block" means that they can not be declared as blockers or attackers. If they are already attacking or blocking it is too late and they will not be removed from combat.
506.4a: Once a creature has been declared as an attacking or blocking creature, spells or abilities that would have kept that creature from attacking or blocking don't remove the creature from combat.
No, creatures that are already declared as attacking (or blocking) are not removed from combat because they could no longer be legally declared as an attacker or blocker. That is only checked when declaring the attack or block, and never again for that combat. This is covered by the comprehensive rules(Emphasis mine):
506.4a Once a creature has been declared as an attacking or blocking creature, spells or abilities that would have kept that creature from attacking or blocking don't remove the creature from combat.
There are effects that will remove a creature from combat, these though all specifically say they do so, on cards like Maze of Ith, Reconnaissance or Illusionist's Gambit. The ways that a creature CAN be removed from combat are spelled out here:
506.4 A permanent is removed from combat if it leaves the battlefield, if its controller changes, if it phases out, if an effect specifically removes it from combat, if it's a planeswalker that's being attacked and stops being a planeswalker, or if it's an attacking or blocking creature that regenerates (see rule 701.14) or stops being a creature. A creature that's removed from combat stops being an attacking, blocking, blocked, and/or unblocked creature. A planeswalker that's removed from combat stops being attacked.
There are also effects that can get around combat restrictions, usually effects that force a creature into play tapped and attacking, this lets you get around effects like Ensnaring Bridge with bigger ninjas, like Ink-Eyes, Servant of Oni, or past effects like Crawlspace by creating tokens when attacking with Hero of Bladehold or Tilonalli's Summoner. If an effect causes creatures to enter with a counter, say Rhythm of the Wild it will also bypass Kulrath Knight that turn.