Let's assume, one of the engines on a twin-jet needs replacement and the jet is is fitted with an old engine and a newer engine after the due replacement, the older engine would tend to produce less thrust at higher fuel consumption due to deterioration on account of aging compared to the new one. Though the aircraft are designed to handle such asymmetries and modern FBW FCS should be able to handle it without bothering the pilot for any manual corrections, logically it makes sense to think one would like to do some basic engine matching to make sure the asymmetry is as small as possible. Do they follow this in real life? Are there guidelines in MRO procedures specified (both Civil and Military Jets) on how to choose a replacement engine, so as to maintain symmetry in the thrust profile?
It doesn't quite work that way. When an engine wears out it's rated thrust doesn't decline; its "ITT Margin" (or some similar phrase - basically its thermodynamic margin at takeoff) declines.
When setting takeoff thrust on a turbofan there is a target N1, or target torque on a turboprop or turboshaft, or Engine Pressure Ratio on a pure jet, and the engine has to achieve that target, so it's making rated thrust or power, more or less, no matter how old it is. What happens when it ages is the temperature required to get there goes up.
There is a maximum hot section temperature (Inter-Turbine Temperature - ITT or Turbine Inlet Temperature - TIT, or Turbine Outlet Temperature - TOT, or something else, depending on where the probe is) for the engine when producing takeoff thrust or power. On a new engine, the actual maximum temperature that you will see will be well below the maximum allowable (the temperature margin).
As the engine wears (turbine and compressor blade erosion mostly) and its efficiency declines, what happens is the hot section temperature when the engine is at takeoff rating goes up. It creeps higher and higher as the engine ages until eventually the margin is gone (or down to some minimum), temperature exceedences on takeoff may start to occur, and it's time to come off.
So there isn't really a thrust asymmetry problem with mixing new and old engines, although there will be a small fuel flow difference, but you have an automatic balancing system to account for this.
Staggering engine times is common. On an older, heavily depreciated jet especially, the engines may represent a huge part of the value of the airframe and it's a common practice to stagger the age of the engines avoid having to change out two at once when they wear out.
What they need to watch out for is applying the right stabilization process (thrust not to be applied in one go), even if both engines are brand new.
Manufacturing tolerances and age affect the acceleration profile and/or idle thrust, and it may lead to veering off the runway.
Any residual thrust difference thereafter would be minimal if perceptible (compared to a light crosswind breeze at best).