@RexRed,
Sure there is. The HL decision was purely based on the govt forcing private industry to provide something they don't believe in. This has nothing to do with paying taxes and how those taxes are spent. Thus THERE is a difference between public and private. The govt is public, HL is private. Paying ones taxes is irreverent to that subject.
Based on the article, would you support someone not wanting to pay their taxes that go towards welfare and other social programs? This is an equivalent question to what the article proposes.