Musical theatre, more often than not, uses head-worn lavalier microphones that are positioned very close to the mouth. This gives a much greater signal-to-noise ratio for the Front-of-House mixer to work with.
These mics are often flesh-coloured so that they are almost impossible to see.
Lavalier mounting in musical theatre is a craft that requires an immense amount of skill to get right, both in positioning the mic correctly from a technical standpoint and also from an aesthetic standpoint so that they cannot be seen.
Popular places to mount lavaliers are on the forehead in the hairline and around the ear and resting on the cheek. Some productions will use a small wire boom that is mounted behind the ear, allowing the mic to be positioned just next to the mouth.
All of these very close positions will give excellent signal to noise ratio. You will still get bleed, but it will be much lower in the signal compared with the direct sound coming from the mouth.
Conversely, TV presenters use lavaliers mounted on clothing, such as suits or shirts. The distance from the mouth is much greater and consequently, the amount of spill in the signal is much greater.