Even as someone who's spoken Spanish from birth and still speaks it now and so should've theoretically mastered it, I've mixed up my genders plenty of times
But then again I sometimes mess up pronouns and names in English with the people around me (calling my brother "she" and my mom "Dad") so maybe it's just that my head stuffing needs changing
Plus my language development was odd so I'm sorta English-dominant now

I can see what you mean about some words matching the stereotypes of masculine and feminine. Volcanos are strong and powerful, while butterflies are delicate and aesthetically pleasing. I personally don't think a lot like that since I'm not a huge fan of gender roles or stereotypes, and linguistically I've gotten used to the singular definite article "the" that fits every word. I mostly guess what gender each word is based on what it ends in, and obviously it doesn't work all the time (el día, el problema, la radio, la canción)

If everything would go my way in my Spanglish speaking world, I'd use "the" for everything and not worry about what gender each word is. I think that if some people adhere strongly to classifying each word to a gender, it's promoting a rigid system of everything being predefined to the standards of the past and the status quo, with not much wiggle room. Granted, that's a bit of a philosophical stretch, but that's how I see it.
Also, it's too much work for me to memorize the gender of each and every word.
So no, in my case at least, the gender doesn't consciously give me an idea of the noun, most of the time. Subconsciously it's still there sometimes, but that might tone down in a few years.

I do wonder what true Spanish-speaking natives would say about this.

As far as I know, the Wall is OK for discussion as long as it's productive and especially if it involves several people, if it turns into a longer, more personal convo between two users it might be better to switch it over to the DMs. But I'm a relatively newer user too.

In most cases I'm personally just used to using one article or the other and don't think about it. In others, however, it's true that I consider some things male or female due to this influence of the language (such as the sun or the moon). In the cases of animals we tend to use their biological gender to refer to them and as a cow will never be male (that would be a bull - el toro) it has the feminine gender, in the cases where the word refers to the animal without taking the gender into account such as el mosquito and la hormiga, there are el mosquito macho and el mosquito hembra, la hormiga macho and la hormiga hembra if you want to refer only to one particular biological gender, so seeing an ant doesn't make me think it should be masculine because I know there are both.

If I were to give every single letter a gender, instead of the all-feminine letters Spanish has, it might be: la a, la b, la c, el d, la e, la f, el g, la h, el i, el j, el k, el l, la m, el n, el o, la p, el q, la r, la s, el t, la u, la v, la w, el x, el y, el z.