I'm a returning player that's new to D&D 5th edition, but I have played AD&D and 3.5e. I've read the core material for 5th. I'm wondering if it's against the class / sub-class make up to use these spells.

Is it okay for a cleric of life to use spells like animate dead and/or contagion?

If it's on your spell list you can cast it

Unlike previous editions, 5e has no alignment restrictions on spells or classes. If you wanted to you could play a Life Domain cleric who solely focused on casting Inflict Wounds.

From a roleplaying perspective you may choose to avoid spells that don't align with your character. However there are no rules that force you to do so.

There is nothing in the rules that prevents it

Whether its "okay" is an ethical and moral decision for each table/player - the rules leave those up to you. If your deity wants to restrict the spells that you cast, that restriction will come to your PC from the DM.

Nothing in the rules stops you, but your god might.

As a Cleric you have access to the full Cleric spell list to choose from whenever you prepare spells. A cleric receives power from a particular god, and this power allows them to cast any spell on the list. You or your god don't need to have a certain alignment or leaning in order to cast any given spell.

However, if you follow a god who hates the undead or imposes restrictions on your casting, you might not be allowed to cast some spells. Some gods put high value on respecting the dead and letting them rest unless you're going for a proper resurrection. An evil god might only let you cast healing magic on his followers or people who are explicitly your allies. The thing you risk should you cast such a forbidden spell is the ire of your god, which can take many forms.

Work with your DM to figure out what restrictions your god may impose. Ultimately, the DM is the arbiter of your game, and they will have to play your god. Make sure to choose a god who will be alright with the spells you want to cast. Your choice of god is generally much more important to this issue than your choice of domain, though the former will probably influence the latter.

Of course, you could end up with a laissez-faire god who doesn't care at all what spells you cast so long as you achieve their goals. If that's the case, you could cast Cure Wounds and Inflict Wounds with the same breath.