B/X D&D and many OSR rulesets use a 2d6 roll modified by charisma bonus to determine whether enemies are hostile, indifferent, or friendly. However, I've always found a part of this nonsensical: the idea of having one trait that makes all creatures respond more positively doesn't really make sense in a fictional way. Here's why:
We can roughly divide creatures one might encounter into two categories: Offensive and Defensive. Offensive creatures include:
• Raiding parties
• Predators searching for a meal
Defensive creatures include:
• Those protecting their young
• Guards on routine patrol
• Animals defending territory
Offensive enemies are more likely to be aggressive towards a harmless-looking enemy but less likely to be aggressive to an intimidating enemy. Conversely, a Defensive enemy is more likely to be aggressive towards an intimidating enemy, but more likely to be indifferent or friendly to a harmless looking PC. To reflect this, ditch the CHA modifier and simply make a note of whether each PC is intimidating, harmless-looking, or neither. Intimidating PCs get +1 to reaction rolls with offensive creatures but -1 to reaction rolls vs Defensive creatures. Harmless-looking PCs get -1 to reaction rolls with offensive creatures but +1 to reaction rolls vs Defensive creatures.
If you want to add even more nuance, give two +1/-1 bonuses to the reaction roll, which either cancel each other out or stack. One of the bonuses reflects your character's appearance, and rarely changes. The other bonus reflects your character's choice of whether to act in an intimidating way or to act in a harmless way. This gives the players a simple element of choice in how the approach an encounter, which can increase engagement. However, they shouldn't always know what the ideal way to approach an encounter is.
If you're playing solo, here's a trick to decide the intentions of the creature you've encountered: use 2d6 of different colors. Call them A and B. If the value of A is greater than B, the creature fits into the offensive category. If the value of A is less than B, the creature fits into the defensive category. If A and B are tied the creature fits in neither category. This creates a fun bit of gambling during the reaction roll.
While it does make reaction roles more complicated. I think the amount of nuance it adds is fairly substantial for the amount of complexity.