Wiring – do about a phone jack protruding from the wall

Is the 4 wire cable the type with 2 twisted pairs? If so, you may have the jacks wired incorrectly, such that the each telephone circuit is using 1 wire from twisted pair A, and one wire from twisted pair B. This would lead to increased and perhaps excessive electrical coupling from pair A to pair B.

If the 4-wire cable does not have 2 twisted pairs, then using a 2-twisted pair cable will reduce crosstalk between your two lines (provided you make sure that line 1 uses twisted pair A, and line 2 uses twisted pair B).

As you have found, traditional US household telephone wire contains two pairs of conductors. This was normally used to allow two telephone lines to be brought into the house, each using one pair, with both lines available at all places to ease switching back and forth or to let phones with additional switches (or, later, circuitry) switch between those two lines.

Red/green was usually the primary line, buy it was common for some wall jacks to swap the pairs so a single-blind phone would connect to the other line.

In older buildings, where the phone wiring has been changed repeatedly, the two lines may have gotten cross-connected in ... creative ... ways. Ma Bell was somewhat notorious for sloppy, least-effort solutions.

(Alternatively. rare now, you may also occasionally see the second pair just connected to a transformer. These were used to power the lights in "Princess" phones.)