The sentence is sloppily composed, though you may hear it spoken. Careful writers ensure concordance by using one of these: These types of people have... This type of person has...
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The PoetMay you also tell me what a non-careful native English speaker would sloppily use?What you wrote in the beginning.
The Poet1. This type of people have an easy lifestyle.2. This type of people has an easy lifestyle.Ah. Well, both—but Cool Breeze's is much more common. The supersession of proximal and notional concord ('people have') is very common among native speakers