Well, why can people trust any other people at all?
Well, here are some ways:
1. They have an incentive to be honest* (e.g. they would be punished if they weren't), e.g. lawyers, engineers, family members
2. They seem like just honest people, e.g. the Dalai Lama?
3. They say or do many other things that you agree with and your values seem aligned, e.g. politicians, athletes, some corporate leaders
4. They are a lot like you, except slightly different, so you trust them implicitly because you would trust yourself
Influencers can hit a bit of all those notes.
At this early point, it's probably easier as an influencer to actually find a place that they like and think are good, rather than just taking cash to promote something they don't believe in. Later on that may change.
Influencers do have a reputation, if they keep sending people to garbage, eventually those people will notice, so they have something to lose.
Some influencers are really good at certain things that people admire (e.g. game influencers), and a lot of influencers go for that 'just a regular person who is your friend and let's go on cool trips together' feel.
But note that these same points are potential reasons to distrust, e.g. an influencer who has hit it big and plans to exit the business anyway may find it more worthwhile to start shilling since their future reputation doesn't matter to them.