Very often I run into situations where characters who have not invested much into social skills are hesitant to participate in dialogues with NPCs.
This has never happened to me.
Are you overly relying on
dice rolls to resolve social interactions? If you ask for skill checks too much, then obviously your players learn that they should not try to do anything that they have low scores at, and just let better characters do it. It's the old rollplaying vs roleplaying gamestyle decision.
I follow the principle that dice rolls are there for
when the DM doesn't want to decide the outcome. I can see that the majority of DMs instead think that almost everything should be decided by the dice, maybe because they have a very simulationist approach i.e. the dice simulates the statistics of inherent randomess of any action.
Take the very iconic situation of having to enter a castle without permission. Typical options (not counting magic) include:
a) convincing the guards to let you in
b) sneaking into without being seen
c) hiding inside something that will be taken in
d) disguise as someone who has permission
e) climb the walls
If your approach is, whatever option the PCs choose,
always have the roll the dice to see if they can make it, then obviously this disencourage PCs to even try something they have low scores at, even moreso if it carries a penalty. So if the party chooses a) i.e. the social option, and they know you're going to make them roll charisma checks, the players whose PC have low charisma might decide to just go grab a sandwich while the others take care of it.
A complete opposite approach (fully narrative) might be: the DM decides which is the winning option, and it's an automatic success when you guess it right, otherwise it's an automatic failure. Most probably this doesn't work well with nearly every D&D player, because D&D does have plenty of stats and mechanics, which are expected to be used eventually.
But why not trying to find a good mix of the two approaches? Choosing option a) can be handled so that, if the players come up with something brilliant to tell the guards, they don't need to roll at all -> automatic success. If they only come up with the usual staple ideas, then sure make them roll, or even decide an automatic failure. The game never says you
must request ability checks. If you always leave a possibility open for winning without rolling, players are more likely to stay engaged in hope of having the right idea at the right time. And that can also be applied to options b) - e) as well!