Natural Strontium is not radioactive.
The synthetic element Strontium 90 is produced in a number of nuclear processes but does not occur naturally. Strontium 90 has a half life of about 29 years and undergoes low energy beta decay. The radioactivity is so mild that your skin would protect you if you held a lump of it.
What makes 90Sr probably the most dangerous component of nuclear fallout is that the human body can't distinguish it from Calcium. It gets built into the bones where its radioactivity smashes biological processes at point blank range.
Tragically, children forming and laying down bone are most at risk. Treatment is difficult because whatever pulls 90Sr out of the body depletes Calcium as well.