Lenses with built in stabilization are a great help to this 'senior citizen' that used to have quite steady hands. As I do a lot of low light shooting without a flash, slightly blurred images happen too often at 1/30th or so without an IS lens mounted. After shooting with both, I opted for the 24-105 f4L IS over the 24-70 f2.8L because of the lack of IS on the 24-70.
With or without IS, a 'stable platform' is always a requirement. Tripods are the most stable, but rather inconvenient and bulky in church or at gatherings. So I typically use a monopod instead. It gives a boost to hand-held stability efforts. If all else fails (or if I forgot my monopod), leaning against a wall or pillar is always better than standing. Kneeling on one or both knees also improves stability. Anything is an improvement over standing. Now if the subject(s) would only hold still for a bit...