I think I understand a bit where your confusion comes from. However, いつ by itself just means the question word “when”. What I’m about to say applies to other question words like どこ (where) and だれ (who), because they work similarly.
When you add も to these, they become sort of ambiguous, in that, while いつ refers to a specific point in time, いつも refers to ALL points in time, that’s why it’s usually translated as “always”. どこも refers to all points in space which is why it’s usually translated to “everywhere”, and だれも refers to all people instead of a specific person, which is why it’s usually translated as “everyone” or “anyone”.
However, this is for basic sentences usually. If you mix other constructions that use も, like in your case いつ来てもいい, the も in the 来ても construction also works on the いつ before, making it effectively a いつも.
いつ来る? by itself means “when will (subject) come?”, and 来てもいい by itself means “it’s ok to come”. By combining them as いつ来てもいい you’re basically making it into “it’s ok to come anytime”.
20代のときは - as for the time of my twenties (marking the topic)
いつ友達や彼氏がきてもいい - “It’s ok for friends or boyfriend to come anytime”
ように - This is a bit harder to translate, but you can think of ように as a way to describe a desired outcome and connect it to an action done for that specific outcome. For example いつ友達が来てもいいように、部屋を片付けた。I cleaned my room SO THAT my friend can come anytime. I think, based on the context mentioned, this is what the person who said this meant, only with the 部屋を片付けた part being omitted because it can be inferred from the context
って思ってた - this marks the previous phrase as something this person thought about, it’s the usual quotation って.
So, to put all the pieces into place, the person, in her 20’s, used to do something (omitted in the sentence but inferred to be cleaning up the room), in order for it to be ok for her friends or boyfriend to come anytime.
Does that help clear up the misunderstanding?