You'll get lots of opinions on how and where to train. They'll be familiar to you, because we repeat the same arguments over and over here, with the usual suspects advocating their same point of view thread after thread. Decide where you come down on those points of view and go with it. I'm going to stay away from that sub-discussion in your eventual response, but, some reactions to some things you wrote:
I am a traditional martial artist...I train Kung Fu and I have a Sifu...
This is how traditional martial artists train. I'm curious if your sifu knows that you've been contacting other clubs and if so has given you advice or guidance on it. If you are contacting other "traditional" clubs, especially non-commercial ones, they may be reticent for a few reasons, including respect for your current sifu.
It turns out l, however that many schools have failed to reply to my inquiries about training - or simply refused to train with me.
I can only share my perspective, but how someone approaches me determines largely how I will respond to them. I don't think I ever fail to promptly respond to anyone who contacts me about training, but I do get emails that I can't really even be sure are legitimate inquiries about training. I posted a thread on one aspect of this last year and got a lot of good feedback that I've taken to heart, but I get emails that say "where r u?" or "how much?" or "hey, I'm gonna stop by your class and check it out. thanx dude." (class times, location, and dues are not published) The short version is that those people are going to have to do better if they want me to take them seriously. It's just not how you approach a traditional martial arts teacher to inquire about becoming a student, especially one who is not after your money. Not saying that you do that, but trying to speculate on why you aren't getting the responses you want.
A commercial judo or MMA or boxing club will probably be more responsive and not care that you have a sifu and are already doing something else.
I am at a point where all the experiences and advice I have been given have led me to stick to my one style. I am a total nerd and love to dig deeper and study the techniques so this is not a problem for me. I just find it interesting how the results of my research and inquiries have led me to this.
When someone approaches me in some reasonable way (there's a broad range, it's not a secret password or anything), but says they already have a sifu and a style, I would have a lot of questions for them about what they were trying to accomplish and whether their sifu supported them branching out and that conversation might lead us to "if you like your style and trust your sifu, I'm afraid that what we do might get in the way of that."
When (happens all of the time) someone contacts me and says "I'd like to learn some Wing Chun, so I can take the good bits and leave the rest of the garbage that you do behind, because I have a special blend of other things that are better..." or some such thing, then it usually doesn't work out for us, because that's not what I'm looking for in a student. Not to mention the fact that it's insulting.
Anytime anyone contacts me for training, regardless of how they did it, I take an interest in what they are looking for and whether or not I think I can help them. I ALWAYS recommend other choices, because I want to train people who really want what I have. And there are other choices and there are other approaches to training. As someone said above, my goal isn't business, it's passing on what was made available to me and trying to help people in the way that I am best positioned to help them. What I do isn't for everyone and I don't change who we are or what we do to accommodate a new student's ideas of what would be better. It's just not how any traditional martial arts instructor who I have ever met operates.
To simplify: Are you advocates of Training one style of martial arts or multiple styles?
This is a different question and you already know the answer. There are traditional martial artists (which you self identified as) and there are modernists. This and every forum is full of the later and if it's balanced with the former then the advocates for modern MMA/mixed-other approaches are going to drown out the traditionalists. I will let the rest of the responses inform you on that question and you'll have to make up your own mind.
I've gone both ways, I spend a lot of my 20s collecting and sparring and brawling and style hopping then settled into a classical system. I also train in a 2nd classical system, but my SiFu had a hand in that, supports it and connected me with it (I have done the same for one of my senior students too). There is a traditional approach to parallel paths in classical styles, but it's not calling around on your own.
Hopefully something I wrote helps you. I probably can't do better in this thread, but if you'd like to DM me and talk more specifically, feel free.