Hi,
The Pure types gladly try their sexuality outside the marriage/aside.
I'd say The Pure types gladly test their sexuality outside marriage. 'Try' is not good. You could say 'try out', except you have the word 'out' later in the sentence. 'Aside' is not OK.
Another way you might talk about this is The Pure types gladly try extra-marital sex.
I find the meaning a little contradictory here. Wouldn't 'Pure' people avoid sex outside marriage?
Best wishes, Clive