Aircraft crossing a runway act as reflectors and obstacles, and therefore affect LLZ/GP/DME beams and signals. Specially when close to the related transmitters, because the relative size of the aircraft is large compared to the beam. In your case crossing the runways can affect the GP/DME of one runway and the LLZ of the opposite runway.
ILS ground protection is described in ICAO Annex 10, volume I, section 2.1.9 of attachment C. ILS sensitive and critical areas (both sometimes known as critical areas) are determined during airport study. They depends on the ILS characteristics (e.g. separate frequency for the clearance signal and number of elements in the antenna array). Critical areas are proposed in FAA Order 6750.16 - Sitting criteria for ILS, e.g. for the localizer:
The ILS critical areas can be protected by fences for area B and by holdings for A, specially for CAT II/III. Such holdings are depicted by a specific symbol:
Aircraft will hold at A12/A13 when the runway is operated in CAT II/III, while AB12/AB13 can be used for CAT I. As there are no CAT II/III holdings on your chart, it means existing holdings are deemed far enough to operate ILS in CAT II.
As for landed aircraft leaving the runway, there are ATC procedures also mentioned in ICAO Doc 013 on all weather operations:
22.214.171.124.1 To ensure that the integrity of the guidance signal radiated by the ILS is maintained during aircraft approaches, all vehicles and aircraft on the ground should remain outside the ILS critical and sensitive areas. The ILS critical areas must be clear of all vehicles, persons and aircraft at all times.
126.96.36.199.2 These objectives are normally achieved by providing appropriate spacing between successive landing and/or departing aircraft. This may frequently be in excess of the spacing normally used and this may affect the capacity of the aerodrome.
To accord with the basic
requirements, the spacing specified should provide sufficient separation between successive
approaching aircraft, normally to allow the leading aircraft to land, to vacate the runway,
and to clear the ILS localizer sensitive area before the following aircraft reaches a point 2 NM from touchdown.
Some States have found that spacing of the order of 10 NM between successive aircraft may be necessary. At aerodromes where the traffic density is low or
where the range of the approaching aircraft cannot be monitored by radar, the separation should be increased to enable the leading aircraft to clear the runway and ILS localizer sensitive area before the following aircraft reaches a point 4 NM from touchdown, i.e. about
the position of the outer marker (or equivalent DME position).
Beams are affected in two ways:
Obstruction decreases the strength of the transmitted signal, but doesn't change the course alignment information.
Reflection and refraction are more dangerous as they create additional paths between the transmitter and the aircraft. These paths are longer than the line of sight path.
LLZ and GP antenna array transmits three signals (CSB, SBO+, SBO-), and a clearance signal, in varying proportion from one side of the LLZ antenna array to the other. Each side can be affected differently, and the alignment, or the linearity, may be affected, due to the phase shift introduced by the longer paths (more on ILS).
The impact on DME is likely not significant as the DME receiver is able to identify the first reply train (LoS) and ignore the delayed ones.