Can I use acrylic caulk around the bath?
Shouldn't be a problem. Keep in mind that unlike silicone, acrylic/latex caulk can (but doesn't always) dry out and crack over time, defeating its waterproofing capabilities, but it's definitely easier to apply and remove/replace.

Most "Kitchen and Bath" caulks are pure silicone, but many people simply use all-purpose siliconized latex caulk like this one: