There is a huge amountof sood research on this subject. And also a huge amount of disinformation and misinformation.
I can give you an answer, which is broadly, yes, there is a possibility, if you already have type-IV allergies to certain chemicals, though it is relatively unlikely.
The biggest danger that has been identified in some studies is over-heating.The crumb gets hot under bright sunlight and can cause minor burns.
There's this research:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5615587/
And this:
https://www.epa.gov/chemical-research/federal-research-recycled-tire-crumb-used-playing-fields
They are from the US, where there has been a strong campaign from a parent following a child's death from cancer. Evidence appears to show that the death from cancer was unrelatedto the use of artificial turf, but the parents do not accept that conclusion.
This study from the Dutch environmental health agency also seems to confirm the 'no identifiable health risk' concluson.
https://www.rivm.nl/en/Documents_and_publications/Scientific/Reports/2017/February/Evaluation_of_health_risks_of_playing_sports_on_synthetic_turf_pitches_with_rubber_granulate