A passive membership interest in an LLC, sold to investors who don't run the business, is generally treated as a security under federal law. Debt-like economics don't change that analysis, and promissory notes can be securities too, so "it acts like debt" isn't the test. Whether a particular offering fits a private placement exemption, and what that exemption requires of investors, is a call for a securities attorney, and there are state notice filings that differ by state.
The accredited-only language in your document is the sponsor treating this as a private offering. In practice that means you'll be asked to represent your status, and depending on the exemption used, verify it with a letter from a CPA, attorney or broker. As the investor you don't need any license to buy. The licensing question lands on the other side: anyone paid a commission for bringing investors into the deal may need to be a registered broker-dealer, and that issue comes up constantly with pref raises done through third-party capital raisers. Asking a sponsor how the people marketing the tranche get compensated is a fair and revealing question.
One practical note on documents. The offering memorandum describes the deal and the risks, and the LLC agreement is what actually governs your priority, your accrual and your remedies. Sponsors sometimes send the first and treat the second as a formality to be delivered at signing. Ask for the LLC agreement early, and read the two against each other, because where they disagree the LLC agreement controls.
