At risk of being told "you have no say in this", I actually find this point of view quite distasteful. As far as I can tell, the summation of biblical law is "love one another". If someone displays that viewpoint and adopts that behaviour, then regardless of their professed faith, how can they be your enemies?
Is loving someone not the exact opposite of being their enemy?
Just my two cents.
Matthew 5:43-44 : "You have heart tht it was said, 'YOU SHALL LOVE YOUR NEIGHBOR' and hate your enemy.' 44. But I say to you, love your enemies and pray for those who persecute you, 45... NASB (all I had close by)
I would encourage you to take a look at that in whatever version you choose as those words are in scripture.
Coming from Jesus^
So you have to take step back and sort of think about what "tough love" is and how everyone wants to give out this "nice love".
There are many different kinds of love as well as different depths, but it is important to come from a biblical standpoint on it.
I may "love my enemy" but what does that love look like precisely? Think about a parent punishing a child for something they deliberately did wrong...taking a away a toy, or "time out", or even spanking (idk if I'll spank my children tbh). It hurts and is painful to the child and my parents used to tell me it hurt them too...
And ^that's just a parent/offspring relationship.
How much more when it comes to someone you call an enemy? To me the parental example is "tough love"
and that we may not like chastisement but it comes from love as per scripture. You can't deny discipline as necessary for a grounded child even with people that have no belief in the Lord so it's a useful way to look at it.
Even in the OT the love of ones enemies is seen as a "courtesy" in 2 Kings 6:20-23.
as well as I would argue the ability for some (except those to whom were specifically excluded for a reason) to sojourn with Israel and become one with them eventually (such as rahab). I'd have to do a bit of digging on the sojourning aspect but you can read Deut. and see that. It talks about them being allowed to join the assembly and the method by which that occurred. Sojourning is somewhat difficult because it means temporary but as with Ruth some choose to stay.
So providing a sort of option in my view is loving in the OT. Tis narrow certainly but that's also what Jesus said.
if this view or scripture is in any way helpful to you I can expound a bit.
As to the OP though I do agree that focusing on the similarities is a good thing if you are missional minded about it. That's where to start, it's a good way to gauge their receptiveness. There is probably such a thing as a "pharasaical muslim" who is completely closed and feels as though they have arrived, I haven't met one but I have seen it in Christianity. The only muslims I have met are either searching, or muslims mostly in name only.
I had a long conversation with a guy that I brought up Jesus multiple times at a bar and we talked about positive and negative forces and things that I define as evil he also did vehemently (as per scripture). It's not even just that it's said in scripture as mere words...it's "inside you". Eventually he told me he was a muslim, and our convo fell off a bit after that because the music got loud and I was just picking up my sister.
I would have continued to look for similarities and not differences and usually when I hit a difference I firmly state my position and what I believe/know to be true and if we can continue, we can.
There are people out there that are open to the truth, it just takes a relationship of some kind. In a neutral setting preferably.
I've heard of some ministries that want you to sort of "breath" in other cultures...like going to a Ramadan feast in order to learn about them in order to witness and I can only say that rubs me the wrong way unless you feel particularly led. I personally would stay away from that. There is a place where things can get so vague and you really want agreement/peace/harmony all around but I don't think this can be. Love can certainly be present though and we can't see all the ways it affects others.
There's no reason to be apart of their ceremonies. To be aware of the and what they are...you can simply ask. It's not about what their religion teaches it's about what it means "to them" and why they do it. I don't need to know what Ramadan is, what does it mean to you? Why do you celebrate it/honor it? Tis a lot more useful because it opens up the conversation.
Neither do I need to observe any other ritualistic activity, I can ask them targeted questions to get a better understanding which allows it to go through my own filter. Feels safer/wiser...
As with all religions, I believe the Lord has people that know him in each one and just haven't "met" him if that makes sense. That's why I'm not opposed to looking if it comes across my path but I don't feel led to just try to convert people. Just listen and be open to an opportunity. I rather like and seek to emulate how Paul preached on Mars hill. Did he have many that were willing to "hear him"? No. But a few, which is cool
A bit tangential but each person is unique and their life isn't something you can understand outside of the Lord's spirit opening that up for you. I think it's
quite important to rest in his leading and to not tread in certain places unless it is clear to you that is what he would have. If you feel an overwhelming burden and are unsure if it is the Lord...my experience has been that there will always be something in scripture to support that.