I'd like to give a little different perspective on this as a regular attendee - I'm more than just a visitor - at another Orthodox parish in my area.
I've got a new fellow I've been seeing for about a month. We're both extremely active in our own parishes. He, however, has duties that make it extremely difficult to get away and he has to arrange for it well in advance. My singing is very portable! LOL. I've been to his parish 4-5 times. I already wasn't a total stranger - his priest knew me somewhat in my capacity as president of a local Orthodox group, plus our priests are good friends and various people attend the parishes for special events, etc.
I tithe at my home parish. I mailed a Christmas donation to new fellow's parish two weeks ago and then I dropped a not unsubstantial check in the plate last Sunday (my first Sunday there even though I'd been there for mid-week/Sat eve services).
As things are going very well with my guy, I've made the decision to essentially split my time between the two parishes - my priest knows and has not objected. That means I will also be donating something to my guy's parish, just not sure what at this time, since I'm trying to pay down debt and save in general. But I'm also providing another voice in their very small choir, which the director much appreciates.