A creature you touch becomes invisible until the spell ends. Anything the target is wearing or carrying is invisible as long as it is on the target's person. The spell ends for a target that attacks or casts a spell.
Emphasis mine. Does touching someone or stealing something count as attacking? Are there other ways to break invisibility beside attacking or casting a spell?
No touching or stealing does not end the spell, as there is no attack roll involved (thus no attack), it is not a grapple or shove, which are special attacks requiring the Attack action, and you have not cast a spell.
The conditions for breaking invisibility are succinct. 5e attempts to have spells do exactly what they say they do, no more, no less, and with no hidden presumptions. You can tap someone on the shoulder or pick their pocket without fear of losing your invisibility.
This is supported in many posts of the lead designer, Jeremy Crawford and succinctly stated here:
A spell's text details the spell's effects—the only thing the spell does. Any additional effects are up to the DM
and here:
Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules.
As other answers have stated, the spell ends if its target attacks or casts a spell (PHB, p. 254). Since touching someone or stealing something are not examples of either of these actions, they will not necessarily end the spell.
You asked if there were "other ways to break invisibility beside attacking or casting a spell". Another way to break invisibility would be to somehow cause the caster of the spell (who may or may not be the invisible person) to stop concentrating on the spell (see Concentration: PHB, p. 203-204).
The spell ends for a target that attacks or casts a spell.
Attacks require an attack roll, or are part of the Attack action.
Touching or stealing is clearly different, and obviously not spellcasting.
