I've never seen an 'IRS Drift' which will take me off an ILS in the few minutes I am tracking the LOC (not since the Harrier GR3's rubber band map system which used to leg it into East Germany at high speed with monotonous regularity)..... + of course, FMC position update negates IRS drift, surely?
Since when you track an ILS with IRS or FMC?...
Anyway, bus skippers here got my point

...and the drift I am referring to is typically as "big" as 1 or 2 degrees.
This drift on the bus, while tracking with the bird, is enough to make you fly within one dot of your LOC deviation scale.
Some people would think they have a crappy handling, but it's not all their fault.
Corrective action:
-Identify the drift: established on the LOC and
accurately tracking your runway track, if your localizer deviation index keeps having a tendancy to go left on your scale, you may have a drift of +1°
-Fly back on the localizer and track now your (RWY TRK - 1°)
For flights within 4 hours, 1° correction should be enough.
Not convinced?
On your next A/P flown ILS, check your Actual Track Symbol (green diamond) compared to the ILS course pointer on your PFD heading scale.
If there is no IRS drift, they should be perfectly aligned.
Most of the time, they're not. You've just noticed the drift.