How would the remote party 'know' if the dynamic IP on your side changes? Does the ISP allow ESP (50) , 4500 and UDP500? I would assume so, because p1 and p2 is up. Check this with tcpdump -> tcpdump -nni any host X.X.X.X
x.x.x.x is remote peer IP. Ask them to send traffic or you send traffic. You need to see encrypted ESP traffic and IKE500. If you see traffic incomming from remote peer you know ISP allows traffic.
Would recommend static IP.
-------
If you like this post please give a thumbs up(kudo)! 🙂