To start with, not all games play the same. Every game has different flows to combat etc; so you can't really stick a one size fits all label on a given role. I think this is a major cause of why people aren't willing to move out of their comfort zone because they're trying to do the same thing they did on another game when ff is different from others. You can deny how things are all you want but you'll probably keep having problems because not everyone is accepting of someone who won't try to adapt to their current situation.
I did look you up on the lodestone and it seems like you're a WHM as your main healer. WHM has gotten some incredible mp management abilities with stormblood and their healing both single target and aoe is top notch to the point of overkill in some cases. There's a ton of information out there that will help you improve and I'm sure most of the people "harrassing" you would be more than happy to help you get more comfortable with healing in this game. If you try to branch out a little bit and at least get more comfortable with the healing part of ff14 you'll probably get alot fewer complaints.
All classes need to focus on multiple things in this game, dps classes get utility skills that require them to target other party members as do tanks. All classes are responsible for monitoring their own enmity and managing it with provided cooldowns. There's mechanics in many dungeons that forces people of all roles to focus on multiple things at a time. I admit that it's not very easy to break into for newer players or people who aren't used to trying to go above the bare minimum of their roles but eventually you'll get used to it. In practice, if you were to simply switch the hotkeys you had your heals on with damage spells instead you would most likely be pushing the exact same buttons you are now with around the same frequency. It's not like people are asking you to go from playing a violin to a 12 string guitar, they're just asking you to hit buttons in slightly different locations.
I wish people would stop feeling "attacked" and "harassed" when most of the time the so-called harassment is merely people asking them to put in a bit more effort or just not ignore 1/3rd or more of their class because of functional fixedness. I've been playing for a few years now and only rarely have I seen what would actually constitute harassment over things like healer dps or tanks using/not using tank stance. There are jerks in the raiding community that go by logs for everything and judge people in all content but most aren't like that. Just like not every healer that doesn't dps or every tank that doesn't drop their tank stance is lazy. When you play with others you have to find a middle ground, that's the basis of cooperation no matter what the setting is. Those that dig their heels in and are unwilling to compromise are wrong no matter what their position is.