"Love your neighbor" and the golden rule
"Love your neighbor" and the golden rule
GR doesn't say anything about motivation; we might follow GR out of habit or self-interest. "Love your neighbor" gives the highest motivation for following GR -- inherent concern for others. So "Love your neighbor" can take GR to a higher level in terms of motivation.
On the other hand, GR provides a workable method to operationalize the vague idea of "loving your neighbor." The method includes developing a factual and empathetic understanding of the other person, putting ourselves in the place of the other, and asking how we desire that we be treated in that situation. So GR gives a concrete way to apply "Love your neighbor."
"Love your neighbor" and the golden rule
No, they're somewhat different in meaning.
Ima Hater doesn't love himself or others; and he's willing that others not love him. Ima follows GR but not "Love your neighbor."
This example suggests that we need to supplement GR (and "Love your neighbor as you love yourself") with the rational criticism of desires.
"Love your neighbor" and the golden rule
They don't conflict if we take GR in its don't-combine form.
GR doesn't tell us what concrete actions to do or what motivations to have; it only tells us not to combine an action (toward another) with a desire (about how we be treated in the same circumstances). This won't conflict with "Love your neighbor."