First no one can answer without knowing what grass strip you are talking about. A firm, flat grass strip of sufficient length SURE. An uneven soft rut gopher hole filled strip... I would not fly on them... Keep in mind the tires both nose and main are small (for low drag). Second to go along with small tires are tight fitting wheel pants that have NO ground clearance, leaving, little room for uneven ground and debris can get caught, jamming inside them. The wheel pants will take a beating. RV'A's of course fly off grass. Some remove the wheel pants and some go further and install larger 6" rims/tires on mains and something bigger on nose gear. A manicured golf course like grass strip almost any plane can fly off. Unimproved rough soft field, the RV's are not ideal and could be unsafe, unless you have tundra tires.
The A models have a history of folding up nose gear and flipping. The original design is OK. However .... poor piloting techniques, bounce, PIO (pilot induced oscillation) can result in a gear fold and flip over as well. This has been beat to death (see old threads), but the original A model nose gears were not super stout. Van has changed the nose gear design going back several years. The new design is slightly heaver and less aerodynamic than original design but should be less likely to fail in the fold under mode. The original nose gear (lower weight/drag/simpler) is still good for smooth grass fields and hard service runways.
I am 100% a tail dragger pilot and fan, RV4, RV7. You can flip a tail dragger on soft fields if mains dig in. However you have more Prop clearance with TG. I believe the RV8A has the most prop clearance of the 2-seat RV's. There are plenty dirt fields I would not operate any RV on. So back to the beginning, marginal field condition, soil softness, surface profile, holes, ruts, tall grass height may make operations not practical or safe. If you want STOL the RV's do well, but they are not Bush planes. Also if at max gross weight the margins are less on small tires which sink further into the turf. Note Bush planes have balloon tires and are typically tail draggers for good reasons.