Rogue: Rogues are the best option for changelings. They are already the go-to class for deception and infiltration, and with the Shapechanger trait they will have just about every tool in their back pocket for that task.
That means changelings have the completely unique ability to have an 18 in an ability score at level one, which means a +4 bonus. Arguably, this makes changelings one of the strongest all-time race choices for Charisma-based casters like Bards, Paladins, Sorcerers, and Warlocks.
Changelings, despite their similarities to humans, live in secrecy among them. Due to their negative stigma due to their natural abilities and racial benefits which make them great rogues, they are often looked down upon by other races and are not easily trusted.
Cleric. A trickery cleric might work, and the Changeling's additional skills help bring you closer to the Rogue's capabilities, but you'll need to balance your need for Dexterity and Charisma with the class's need for Wisdom.
Races & Adventurers
The Traveler is the patron of all those who welcome change, in body and in philosophy. Its worshipers include changelings, shifters, doppelgangers, and lycanthropes, who see it as the greatest of gods, but only doppelgangers and lycanthropes routinely revere it.
Changelings typically have large eyes with narrow pupils, ranging in color from white, to yellow, to black. Hair colors are similar: Light grey, platinum blonde, shades of silver, all the way to the darkest hair color being a light brown.
WotC has confirmed that changelings are considered to have the Shapechanger subtype. So they are indeed immune to polymorph and can be affected by moonbeam.
The short version is that a Changeling can shapeshift to a form that can produce sperm to impregnate someone, and can shapeshift to a form with a uterus and eggs to get pregnant, but a pregnant Changeling cannot shapechange to a form without a uterus without ending the pregnancy.
Changelings are thought to be an uncommon race—though their true demographics remain unknown, as may live their entire lives masking as other sentient races. Many places in the world fear changelings for their unique ability to assume the form, or 'profile', of nearly any person, indefinitely.
Most often, the mother begins to carry twins, and one of the twins is a changeling. There are extremely rare cases of being born alone, or as part of triplets. In the rarest of cases, the other twin is a hag.
Changelings are bad. The person who leaves infant Bloom in the human world does so knowing it is at minimum, culturally unacceptable, and possibly breaks some laws. The way kids treat Bloom when they find out she's a Changeling is similar to the way kids treat Harry Potter when they learn he can speak Parseltongue.
A changeling can alter his or her gender (and reproductive abilities) as part of using the race's minor shapechange ability.
You only get one of those and you can never change your class with it. It is just a particular person (race, gender, age, appearance, etc) you become that has a tool proficiency. You can have as many personas or masks as you want but only one of them has the proficiency (and always the same one).
Changelings have red blood like a majority of the other races. Bleeding around others may alert many that the Changeling is not of the same race (should the blood color vary). For this reason, a Changeling will usually choose to take the form of a race with red blood.
17. As a playable race, changelings have the following abilities: Shapechanger: Using an action they can change their appearance and voice at will, even adapting their size between small and medium in some cases.
A changeling can alter its appearance. It can conceal existing scars or tattoos, or add new ones. So the tattoo will exist, but the changeling can hide it.
Changelings lay their eggs directly within food sources her offspring will eat after hatching - namely stashes of meat - that the mother has procured and hidden out of sight in a secure place, such as the abandoned burrow of some small animal, a crevice in rock, or a small hollow in a tree.
DS9: "Chimera" suggests Changelings have a lifespan of at least two hundred years, although if Odo was indeed two hundred years old when he traveled back with the USS Defiant in an alternate timeline in DS9: "Children of Time", that would indicate Changelings could live for at least four hundred years.
Most often it was thought that fairies exchanged the children. In rare cases, the very elderly of the fairy people would be exchanged in the place of a human baby, so that the old fairy could live in comfort, being coddled by its human parents.
Changeling blood is green, unlike most other animals. Changelings, despite their thinly and seemingly fragile frame, are capable of surviving otherwise fatal injuries thanks to their magical abilities.
Changelings need to sleep like everyone else after all and if they always reverted to their natural state when sleeping they would have one hell of a time staying hidden. A sleeping creature is considered unconscious in 5e at least.
Changelings born from two changeling parents are born in their natural form: pale, slender, with colorless eyes and white hair.