Can asking for travel and equipment support hurt a grant application?
I think you are looking at this from the wrong side. Funding agencies typically won't care so much what kind of costs your project accrues, but rather how large those costs are in the end. That is, if there are two scientifically comparable projects, but one is much more expensive than the other, this will make the cheaper project more attractive to fund than the expensive one. Whether this cost discrepancy is due to higher personnel costs, or due to other factors, won't be central to the decision.

However, multiple factors make your question whether you want to ask for equipment and travel less important than what you might think:


At the end of the day, the costs of equipment and travel are typically very small in comparison to personnel costs, so this is unlikely to make a big difference for most grant types.
The case that two projects are so similar in terms of scientific merit that relatively modest equipment and travel costs have an actual impact and the agency cannot fund both projects is not very common.
Many agencies (at least here in Europe) reserve the right to cut down on your budget if they think it is over the top. That is, if your project would be ok without equipment and travel, they may end up just funding the project but not granting the equipment and travel money. This is particularly common if your proposal does not make it clear enough how this money is essential to the execution of the project. At the end of the day, everything that kind of seems like a "nice to have" cost is very likely to not be granted.


Summary: worry about your proposal. Don't worry about equipment and travel costs.