In the proficiencies of Druid, it says Druids will not wear armor made of metal, however, if I was originally a ranger, can I still wear my metal armor or do I have to remove it?
In the PHB pg 164 it gives you the multiclass table for what proficiencies you gain once you place 1 level into Druid (or any other class). Note on this table it also reminds you that Druids will NOT wear any armor or use any shields made of metal, just like it does in the Druid section earlier in the book. Thus your answer becomes: No, you may not wear your metallic armor you wore as JUST a ranger, and must remove it if you wish to become a Druid and use Druid powers.
It could be thought of like this: You were just a Ranger, and had no qualms about using metallic armor. You were curious to learn the ways of the Druid and have realized that before you can properly harness druidic magic and the abilities of Wild Shape, you must first take a vow to never wear metal on your person. Then the local Druids will teach you what you want to know.
From the proficiency section as you pointed out:
Druids will not wear armor or use shields made of metal.
My interpretation of this statement has always been that it's not that druids can't wear armor, they just won't. So if you choose to wear metal armor, you're choosing not to follow all the tenets that make druids druidic, and thus choosing not to be a druid. Reading over the "Sacred Plants and Wood" section on pg. 66 of the PHB, it talks about how a druid holds certain plants sacred and picks specific woods for arms and armor based on the characteristics of the wood. For example, oak is associated with strength, so a druid would make a shield out of oak in order to tap into that quality. As an extension, druids do not hold metal sacred, so why would they use it?
So to answer your question more directly, no, you may not wear metal armor since no druid would do that. I could also see a DM saying that if you are a mutliclass druid and actually donned metallic armor, you would lose all your druid abilities until you removed the armor.
You're still proficient in metal armor and may wear it. The negative consequences are:
Your druid is passionate about naturalism — it's literally his religion — so he tries to avoid non-natural things when he can.
Druids don’t lack the ability to wear metal armor. They choose not to wear it. This choice is part of their identity as a mystical order. Think of it in these terms: a vegetarian can eat meat, but the vegetarian chooses not to. (Sage Advice)
It weakens your druidic connection to nature and thus abilities reliant on it. This follows from the RAW rule that druids who grossly violate their principles lose all druidic powers,
A druid who ceases to revere nature, changes to a prohibited alignment, or teaches the Druidic language to a nondruid loses all spells and druid abilities (3.5e SRD)
, with the RAI interpretation that druids have a weakening connection for violations against nature. Sage Advice explains that this is really a story issue that'd require DM management.
If you feel strongly about your druid breaking the taboo and donning metal, talk to your DM. Each class has story elements mixed with its game features; the two types of design go hand-in-hand in D&D, and the story parts are stronger in some classes than in others. Druids and paladins have an especially strong dose of story in their design. (Sage Advice)
Your Wild Shape ability can't meld large chunks of metal into your new body, so you can't use it while in metal armor. As with the above, this follows from the RAI interpretation that druidic abilities don't work with things that druids aren't supposed to do.
Your druid can interact with and even wear metal without suffering from any special weakness due to being a druid. That is, you haven't acquired a weakness to metal by gaining a level in druid; you merely don't enjoy the full benefit of being a druid while disconnected from nature.