Well, respect is one of those nebulous and vague ideas that are hard to pin down even though they're used in everyday life. In some ways it measures esteem and in others deference, and you have respectability and respectfulness, respectively (snort). Though I wouldn't mean to imply they're distinct categories, it could be useful to distinguish between respecting someone and showing respect to them; generally the latter follows the former, but not necessarily. You might respect an older family member's wishes in order to show respect, while also thinking they're a dickhead (there's an element of ingratiation or perhaps social self-preservation). So respecting someone is your own internal measure of their character, whereas showing respect is an external act. Along the same lines, you could distinguish between lacking respect for someone and disrespecting them. (I suppose it's not necessarily a person, either; it could be a group, a place, a custom or and institution - not talking loudly in a church, for example). It also seems mutually reinforcing, so if someone shows you 'respect' you're more likely to show them 'respect'. And it goes the other way too.
I guess respecting figures of authority - older people, especially family members; clergymen; policemen and the judiciary, etc - is a big one. Which also reveals a lot about disrespect - how you address them stands out. Generally using the appropriate terms or tone is the criterion of showing respect. So you say 'Hello, officer' rather than 'What's the story, bud?'
Unfortunately, some people interpret disagreement or disobedience (for lack of a better word) with disrespect, in much the same way that some people take any kind of criticism as a personal attack. I'm sure everyone has had an exchange with a parent where you were accused of 'disrespecting' them in a way that seemed extremely unreasonable and essentially a defensive reframing of the narrative on their part.
But back to respecting someone in a more internal sense, like you're suggesting when you talk about other people's ideals. Personally I feel respect toward people who possess what I would consider certain virtues - politeness, patience, kindness, conscientiousness and most importantly consideration for others, which I think is key. Other kinds of ideals (for example, having different political or religious beliefs) seem less important (unless they undermine the former values). But naturally that reflects what you consider to be virtues, too.
Basically if you're a nice dude, I'll probably respect you, whatever that actually means; if you're a bellend, I won't.
Showing respect, meanwhile - I won't put my feet on the table in your house.
Having written this comment, I feel like I'm in more of a mess than when I started it! This is really difficult terrain to navigate.