「よいことをする」という気負いがない分、自然体でボランティアに関われる人も多いのです。 Can someone explain the meaning of this? From what I see: > 'doing good thing' in other words NOT being enthusiastic, these type of non enthusiastic people are a lot?

* is not "in other words". Please read this and get used to how it works.
* This means "pressure put on oneself" or "(negative) self-consciousness" rather than "enthusiasm". (The definitions from jisho.org are admittedly misleading. refers to "It's _MY_ job" kind of eagerness/pressure, not enthusiasm in general.)
* is "natural stance", and roughly means "like one's regular self".
* is "to the extent" or "the more the more ".



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> There are also many people who are engaged in volunteer activities in a natural manner all the more because they have no self-imposed pressure to "do good things".