Tests you only partially trust are a lot better than no tests at all.
Also, the tests can be less reliable by generating false positives. As long as all positives are checked, and the tests are maintained to pass (by fixing the tests and production code as needed), then false positives are not going to hurt your production code's reliability.
As long as your less reliable tests are not generating false negatives, you are fine.
Also, the tests can be less reliable by generating false positives. As long as all positives are checked, and the tests are maintained to pass (by fixing the tests and production code as needed), then false positives are not going to hurt your production code's reliability.
As long as your less reliable tests are not generating false negatives, you are fine.