Yes, the plug is being pulled on Google Reader in July. If you happen to use Google Reader to read blogs in one place, you will probably want to find another reader, but there's no hurry. If you don't use Google Reader, carry on as normal! Whatever the case may be your own blog is safe, and it's still at the same web address it ever was.
So don't panic when you read references to "claiming" your blog! Claiming in this context is not staking out a claim, reserving a space, or anything like that. If you do currently use GR to read your blog subscription list and happen to want to switch to Bloglovin, you may be curious to know who is reading you using Bloglovin. If you have "claimed" it Bloglovin can send you info about who is subscribing to it, but your blog won't disappear if you don't claim it on Bloglovin and others can still read it on Bloglovin or anywhere else.
When Bloglovin talks about claiming, what they want is to be sure that you are the owner of that blog so they can send you stats on it. You know if you subscribe to a newsletter by email, you enter your email address, and generally you receive an email in which you have to click a link to verify your email address and activate it - it's kind of like that.
When you follow their procedure for claiming you end up with a link in your post inviting others to follow you on Bloglovin. That doesn't mean that you now exist only on Bloglovin, it's just a clever bit of advertising on their part. And if you see this link on a post by one of your favourite bloggers, you don't have to click it! You can still find and read them wherever you like.
So take your time looking at Readers to decide which interface you like best for reading your own list. That decision is the only action you have to take and you don't even have to do that if you are currently happily reading blogs some other way. No decision you make affects how anyone else reads your blog. You don't have to "be" on Feedly, Bloglovin or anywhere else!