I think it's important sometimes too to keep in mind/watch out for those folks that loudly proclaim they're being shut out in public, when you know you've bent over backwards to include them, and that sometimes you will be called out by those folks no matter what you do.
I loop people into +jobs, post information as I get it, scene with people about it (though frankly this is reciprocated so rarely I'm always shocked!). And yet, I know now from experience not just on TR but elsewhere that you will still have a handful of people who will say that 'everyone' is 'shutting them out' esp. on staff jobs (even though as most of us know, a lot of times the holdup is slow staff response that simply cannot be helped, and yelling at the players who are also working on it might feel good to the yeller but does nothing at all except for make the wrong people feel bad). Or there will be some acknowledgement that you are trying to loop people in, but now you're controlling/not Doing It The Way I Need It.
So by all means, it's important to at least OOC info share if the culture allows it IMO. Or ask how people feel they'd best be utilized or be looped in! But realize that especially for 3rd party (not you) controlled plots/PrPs that there is a limit to what you can do, and being willing to take on the role of trying to get folks involved/being generous with your info also quite a few times makes you a target (like the customer service rep is a target--you're just the person that they're talking to about their frustration, and even if it's truly not your fault, you are probably going to be the recipient of a lot of vitriol when they're frustrated). I think that is why /some/ people are reluctant to really be open to including folks they don't know.
As an ST I have more control, and I can ASK people about their connections/character. I think the key to involvement as an ST is to make it personal/relevant/tied to the PCs involved. It takes a little more communication sometimes than generic Kill This Here stuff (not always though, and generic plots sometimes give you an insight into the PCs that you can file away for later).
I find it hard to ask for RP. Everyone's got their frailties, and my biggest one, frankly, is rejection. I always assume that people would rather RP with other people than me. I find it hard to join scenes already in progress even if they're public because I just know that I'm bothering people with my lame ass poses. I get flustered easily. 20 years of doing this and it hasn't gotten easier. I feel butterflies in my stomach when ever I ask on chan or even privately for play, even if I know the other person likes me.
But here's the thing. If I want to play, it's still ultimately on me to reach out. IT would be really nice if all those other people would do so, but for all I know they feel the same way. So I make myself do it, rather than assume that they're all ignoring me/hate me/passive aggressively sigh and mope on channels, ect. And sometimes other people do that and I get a break now and then in asking. It's just how things work. I find fair or not as I get older, I find it harder to deal with the hothouse flowers who even state openly on channel or in finger that they'll never ever ask you for RP because they're too shy. (To me, that takes more brass balls than I ever will possess to proactively declare to everyone it's all on them to make sure they get to interact with me, because it's out of my comfort zone. So I admit I will tend to avoid those folks because in my experience not only do they want to be paged first, the only RP they accept is where you are trying to 'draw out' their cool and deep character while very little reciprocity is given and they tend to assume that friendly PCs/PCs of this and that type are just shallow compared to them, ect.)
For me though involvement is largely about ooc attitude. I think having a friendly and open attitude helps lots. I understand why people don't, but if you wall yourself off or make it so that people have to work really really hard to get you involved, and you don't show initiative, I think that can make some of that a self-fulfilling prophecy.