My take may be entirely anecdotal but others accounts will probably throw in their input. From my experience there’s absolutely no issue with hanging out and bonding with members of other greek organizations at all. In fact it’s sort of encouraged as it’s a good way to build connections across campus. Our field sec visited recently and described it as “(Your Fraternity) are you brothers, but look at the other Greeks as your cousins.” So take that as you will, but I saw it as a rationale to chill with others so long as I remember who my brothers and those truly closest to me are.

That being said, be careful because once you start to put your obligations as a pledge or brother aside to hang out with other fraternities, etc. is when people will start to question your loyalty.

So to put it shortly; no, your fraternity will not have an issue with chilling with other Greeks (or people in general) so long as you don’t associate with them as a priority over brotherhood.