I have an S-RJ01 plugged into a router and it will not work when connected to a TP-LINK router LAN PORT, it will work if connected to a MikroTik router LAN port, nothing else has a problem getting an IP address and allowing connection to Internet

There's no such module.
It's either S+RJ10 https://mikrotik.com/product/s_rj10
Or S+RJ01 https://mikrotik.com/product/S-RJ01
Read the info provided for each of them.

It is an S-RJ01, see picture

Before you fix the title and the question, you wrote wrong: "S-RJ101"
it's ambiguos
that's why @Znevna wrote that

I have plugged it in to a Ubiquiti UDM-Pro so I can use the built in failover backup but it will only communicate with MikroTik devices, ( Routers Switches ), it will not communicate with anything else i.e. TP-Link routers, not even a Cisco router, is it faulty or is this by design?

Not actually made by MT but for MT by a generic maker so it should work. Strange......

I have discovered the problem, it will only communicate with gigabit ports on other devices when used in a Ubiquiti UDM-Pro and the ports on the other routers I was connecting too only had 100Mbps ports, that is why it was not working, now it is connected to a BT smart hub it is working, need to put smart hub in to half bridge mode now.

I have discovered the problem, it will only communicate with gigabit ports on other devices ...

Apparently this module does not work with all devices. I tried to connect it to my old switch - Allied Telesis GS950/16. The result is negative. 1000X SFP Ports

I Used a SFP to RJ45 Media converter fitted with another RJ45 module to connect it to a 100Mps router and it worked fine

If you check the compatibility list, you'll see that it doesn't work at 10/100 in some devices: https://wiki.mikrotik.com/wiki/MikroTik ... ity#S-RJ01
And of course TP-Link isn't listed, because obvious reasons.