The popular dairy alternative oat-based drink (OBD) is made from hydrolysed oat. However, natural OBD is inherently unstable. OBD is commonly made from wholemeal oat and considered to have health benefits due to the β-glucan content. β-glucan is also a hydrocolloid with stabilizing potential and stored mainly in the bran. This study investigated the effect of bran substitution, to traditional wholemeal oat on the stability and physicochemical properties of OBD. In addition, the effect of the loss of the β-glucan network at neutral and acidified pH are also assessed. Products with intact β-glucan from bran were highly viscous and, thus, stable throughout storage at 20 °C for 14 days, but showed a viscous gel-like tendency that is unsuitable for thin beverage applications. The loss of the β-glucan network made thin beverage-like products that were unstable. The instabilities observed were phase separation due to thermodynamic incompatibility (bran pH 6.4), gravity separation-based creaming (wholemeal pH 6.4 and 4.2), and electrostatic complex formation (bran pH 4.2). The complex formation highlighted the slight anionic tendency of hydrolysed β-glucan. The use of bran fraction leads to higher protein and β-glucan content. The physicochemical balance of the products greatly influenced the stability of the product.