Word that describes terms that exclude or divide people

Within the specific contexts of these scenarios we might describe these words as controversial. Perhaps the individual words could be described more specifically as divisive. In each case, one person used divisive language which discouraged the other person from wanting to participate. I would argue that the words could be considered divisive because they are often in complete contrast (to the point of being offensive) to the other person's view.

divisive /dɪˈvʌɪsɪv/adj. — Oxford

Tending to cause disagreement or hostility between people: 'the highly divisive issue of abortion'

Here's two adjectives that may be useful for the contexts you've included.

contentious adjective: causing or likely to cause an argument; controversial. "a contentious issue"

synonyms: controversial, disputable, debatable, disputed, open to debate, vexed "a contentious issue" see, Google.com contentious

coloured adjective: 1.1. Imbued with an emotive or exaggerated quality: “highly coloured examples were used by both sides”. Oxford Dictionaries colored/coloured

Issues like abortion and evolution are often described as Divisive.

I think in the context you describe it would be acceptable to describe the language tied to those issues as divisive.

If you want to describe a situation where a minority group or an individual is being excluded, rather than one where a group is divided into factions then you might use the word exclusionary.

Not a single word, but an expression I would use for this sort of situation is "His comments put a wedge between them."