Regarding the postulates of the kinetic theory, in one place I read:
There are no intermolecular forces except during the collision between molecules.
And yet in another place this appears:
Collisions between two molecules do not exert unattractive or repulsive forces.
Aren't these statements contradictory? Are there or are there not intermolecular forces during the collision, according to the postulates of kinetic theory?
The kinetic theory of gases is, empirically, a good approximation to how most gases behave most of the time. Its key assumptions are:
The two statements you have are (especially the second) are poorly worded versions of these assumptions. For the collisions to be elastic there have to be repulsive forces between the entities that make up the gas.
But don't forget that the assumptions are not strictly true, they are just good approximations under most conditions. Molecules are not infinitely small and attractive forces do exist. But, at least when most gases are far from the point where they liquefy, the approximation is good and it explains the way gases behave. For example, a given quantity of a gas (specifically the number of molecules or moles) always takes up the same volume at the same temperature and external pressure however big or heavy the component molecule or atom is. We observe this to be true (approximately).
The apparent contradiction you worry about is due to a careless way of stating the key assumptions and is not a problem with the (well validated) theory.
I tried to find the place where you found the two statements, and I could not.
Absence of long-range forces
The first statement makes sense to me:
There are no intermolecular forces except during the collision between molecules.
The OpenStax Chemistry textbook, for example, has this statement:
Gases are composed of molecules that are in continuous motion, traveling in straight lines and changing direction only when they collide with other molecules or with the walls of a container.
Both statements say the same thing: there are no long-range forces acting on the particles.
Elastic collisions
Your second statement does not make sense to me, and I think it contains a typo.
Collisions between two molecules do not exert unattractive or repulsive forces.
The corresponding statement in the OpenStax Chemistry textbook is:
Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic (do not involve a loss of energy).
This statement also does not make sense to me. If there are collisions, there are repulsive forces. The second part is a known component of kinetic theory. The particles can exchange kinetic energy, but the total kinetic energy is conserved (or more stringently, momentum is conserved).
What were they trying to say?
Two billiard balls hitting each other are a good model of an elastic collision. Two balls covered in velcro are not - they are sticky. So in that sense, you want an absence of attractive interactions so that particles don't stick together (and form a condensed phase). I am puzzled why they think repulsive short-range interactions are incompatible with elastic collisions. Even attractive interaction are compatible with elastic collisions when they are sufficiently weak that they break when the repulsive interactions push the particles apart after colliding.
How do molecules actually behave?
Molecules have attractive interactions at short range that turn repulsive when they come too close together, for example modeled by a Lennard-Jones potential for noble gas particles. A substance like water make hydrogen bonds at short range. Using water as a example, these interactions are not magically turn off when liquid water turns into a gas. Instead, they become negligible because the molecules have high kinetic energy (or for low pressure, the number of collisions decreases compared to normal pressure). So for a gas much hotter than its boiling point, we can neglect those interactions and still get a good explanation of the temperature vs. pressure behavior.
