'in their activities' is correct and usable in written English.
You can use it to refer to something people are doing. For example: The students are showing great enthusiasm in their activities.
Still, modern-day politicians can feel relatively safe in their activities.
These criteria ensured the groups were active in their activities and reasonably represent a cross-section of community opinion.
Mr. Tajzadeh has other friends that were active in the party headquarters and they still continue in their activities.
And she participated fully in their activities.
The colectivos vary widely in their activities and organization.
She could not be involved in their activities.
When the three strange women first appeared, Mrs. Kibwetere at first joined in their activities.
Almost all outfitters want participants to sign agreements acknowledging the "inherent dangers" in their activities.
They have to be selective in their activities and can't take on the whole globe.
Far-right extremist groups have become more vocal in their activities.
