Can Hyaluronic Acid cause skin redness and inflammation?

Short answer is: yes, it is plausible. If your skin is reactive and sensitive, prone to redness and small inflamed spots, a product with hyaluronic acid might be the issue.

Not all hyaluronic acid is created equal. We have two types of hyaluronic acid present in our skin naturally: a high molecular weight (big molecules) and low molecular weight (small molecules) hyaluronic acid.

The big molecules of hyaluronic acid (HA) are part of the top layer of our skin where they help the skin create and maintain an effective protective barrier. They help attract water to the upper layer of the skin keeping it supple, flexible and what skincare marketers usually describe as "radiant". Applying high molecular weight HA to the skin topically can support skin barrier function through attracting moisture - as long as the application is combined with an emollient (for example, an oil or silicone) to “seal it in” (if HA is applied to the skin on its own in a dry environment, it can pull water out of the skin leaving it drier). 

The small molecules of HA are also naturally present in our skin. They are created as the result of destruction of the big HA molecules in presence of inflammation or injury.

The small HA molecules can trigger skin’s immune defense mechanisms promoting cytokine production (that is creating more inflammation that can help skin fight infections).

While dermatological studies confirm that low molecular weight HA stimulates inflammatory response in skin, there is no evidence that applying it concentrations usually used in cosmetics does in fact cause inflammation. Still, it might be prudent to stay on the safe side and opt for high molecular weight hyaluronic acid in skincare, especially if your skin is sensitive. 

How can one tell which type of HA is used in a product? Paradoxically, skincare brands typically advertise loud and clear if they are using a low molecular weight HA. The thing is that this type of HA is more expensive and can penetrate deeper into the skin, and it is often automatically seen as a benefit. So if you want to maximise the chance of buying a product with high molecular weight HA, go for not expensive brands with simple formulations that either specifically disclose that they use big molecules of HA, or do not advertise the type of HA they use (this, most likely, will be a high molecular weight one).

Sources: 

Hyaluronic acid applications in ophthalmology, rheumatology, and dermatology https://www.sciencedirect.com/science/article/abs/pii/S0008621520300124

A Low Molecular Weight Hyaluronic Acid Derivative Accelerates Excisional Wound Healing by Modulating Pro-Inflammation, Promoting Epithelialization and Neovascularization, and Remodeling Collagen https://www.mdpi.com/1422-0067/20/15/3722

Hyaluronan in wound healing: rediscovering a major player https://pubmed.ncbi.nlm.nih.gov/25039417/