Agreed about adopting each other's interests and developing new ones together. bringing people together. (Though the pattern I see is women adopting the guy's mountain biking and rarely the man adopting the woman's interest - if it is sport men can't deal with a woman being better than them and if it is not sport, then, err, ahem ...)
Questions to ask though:
1. Are you being invited in? "I usually go for yoga Tuesday evenings, will you join me?" as opposed to "I can't meet Tuesday because I have a yoga class."
2. At least at the beginning, do they reduce the frequency of their activities in order to spend time with you? Assuming that most healthily independent people find ways of filling their time when they are not in a relationship (even if it is just sitting and reading), when a relationship starts something has to give to make time for it. (And if that time comes only from all the other dating the person is not doing, that might be a sign of a non-introspective or non-interesting person.) As an example, "Since you are free on Tuesday and everything else looks difficult, I'll either skip climbing or find a different time I can do it!"