If I were to share my ifconfig information from Linux publicly, is there any possible danger associated with this action?
There are at least 3 dangers:
Sharing your public IP addresses - it will surely result in several kinds of unauthorized security scanning (this applies, if your servers have public IP addresses).
Sharing your public IP addresses combined with possible OS version (ifconfig results on different OS-es look differently, you can compare ifconfig from modern Linux with ifconfig from BSD, or with typical Linux from eg. 2004). This is dangerous, if you are forced to use old software for some reason.
Sharing valid MAC addresses - a few years ago I read an investigation report about some fraud, which - apart of the most important facts - used changed MAC addresses on computers, where these MACs were changed to imitate valid MAC addresses gathered from competitive company's computers, just to mislead the investigation. I have completely no idea, how popular might be this kind of misleading activity, but I wouldn't publish my MAC addresses, just for sure.
It depends on the type of IP information you are sharing. If you are sharing this information for a NATed network, such as a 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0.16 you should be fine as long as you are not sharing other information such as the company name, hostname, etc.
IF YOU ARE DOING THIS FOR A MACHINE THAT HAS A PUBLIC IP ADDRESS, DO NOT SHARE THIS INFORMATION FREELY TO THE PUBLIC!
I have seen this lead to a mess including DDOS attacks, unauthorized vulnerability scans, etc.