Minor aspects in their primary mode, are mostly active in transiting astrology, current planets moving over your chart, triggering specific fated events which merge the two natal planets features together and so on. In a secondary light, yes, inconjuncts and so on do figure in the Natal chart proper so long as the degree is tight, outside of 1 degree I'd say it would be harder to exactly pin it down. Outside of 2 degrees it's not a minor aspect. They are definitely important, but determining the detail of their importance you have to look at the signs both planets of the aspect are residing in, determining the amount of their importance is in the tightness of the aspect and the nature of the planets involved.
Moon inconjunct Pluto is an emotional aspect which indicates fated events that relate to intensive and fixated energies concerning the Mind and the affairs of all of the houses ruled by either of the planets. Say transiting Neptune is moving over your Natal Moon without Pluto involved. This would trigger Mental hypersensitivity for the time of the transit, and potentially fated events. If the Natal Moon instead is also contacting Pluto in this way, it would mean that transiting Neptune is also involved with Pluto, which increases the likelihood of fated events. This transit would also be more transformative, perhaps a period of realising past life experiences, remembering who one is or even acting out on past life impulses positive or negatively, it could also indicate for that time, an emotionally intensive grip on you which leads to definite insights into unique and personal things, which others with differing natal charts might probably never bother with dwelling on, or if they did, would have to build up that same intensity through their own meditative practices to come to the same point of understanding. Another one with this is observing your own neurosis' and underlying fears (which all of these planets particularly Pluto, are to do with).
This is the same as experience is the best teacher, and there is always the soldier and the senator- different people will forever learn different core things about existence more naturally than others. E.g One with Pluto in another sign, with a different Pluto aspect to the Moon dealing with this transit, means that Pluto instead works its way into the insights of that other particular sign. Say if your Moon inconjunct Pluto has the Moon in Aquarius and Pluto in Virgo, this hypothetical Neptune transit would garner different mental experiences and insights than one who had Moon in Aquarius but Pluto in Cancer instead right? Or others with the Moon also in an entirely different sign which constitutes an entirely different foundation of their mental nature to begin with.