I believe the main difference is in the way of “acquisition” by the person:
most people receive the certain religion being children, within their family. Child perception is non-critical, so the religion incorporates into her/his system of values freely.
People chose the certain ideology in youth or, being adult, i.e. in more mature condition. It implies their responsibility for their decision.
The intermediate case of ideology-directed lesson in the beginning school is very dangerous, because here the ideology takes the advantage of religion.
The western society is still much more tolerable to religions than to ideologies,
despite the fact that in 21 century much more people have been killed because of religious reasons than because of ideological ones.
Very rare that I see this kind of analysis. I’ve been saying this for years. Both religion and ideology are based on _belief_ systems which are merely forms of ignorance and magical thinking.