A lot of small non-profits are “sort of ” sketchy in that the people running them are also deriving their parnassah from them. As long as people (donors in particular) understand this (e.g. a shtiebel in which the Rav runs the shul and gets most of his livelihood from donated money) it is as much an ethical problem as a legal problem since the government expects non-profits to be run by independent boards who hire staff (rather than by staff which recruits a friendly board).
This is common throughout society (not just Yidden). As long as the person running the non-profit is doing a good job providing services, and sticks to a modest lifestyle, there is no problem.
The alternative would be to have big, quasi-government, bureaucracies doing the same job, and they would probably be less efficient and less responsive to needs of users (just look as the “non-profit” hospitals with seven-figure salaries for managers).