If it's strictly informal bartering labor for a campsite, you would stay under the legal radar. However, many workamping gigs pay wages and then charge you for the campsite. That may net out to be "free campsite for services", but it creates taxable income in the US and is a legal problem if you are supposed to be a non-working visitor to the USA.
Technically, any barter arrangement is taxable, but a tax loophole allows an employer to provide an onsite living arrangement under certain conditions. If the loophole conditions are met, the campgorund does not have to report the value of the barter as employee income. Some workamping arrangements may qualify for that loophole, but many (most?) do not.