This works for me if I use curl -L..it seems like Twitter is redirecting to HTTPS, but if you're not following the redirect you get nothing. I can confirm that specifying HTTPS via curl https://twitter.com works as well.

Based on that, it's unlikely this is a routing issue, but if you choose to go that route in troubleshooting, MTR is going to provide much more info than traceroute:

https://linode.com/docs/networking/diagnostics/diagnosing-network-issues-with-mtr/

Thanks smallclone. Unfortunately I'm either just not doing it correctly or else it's still something else wrong.

~ ♖ curl https://twitter.com
curl: (7) Failed to connect to twitter.com port 443: No route to host
~ ♖ curl -L https://twitter.com
curl: (7) Failed to connect to twitter.com port 443: No route to host

I'll start looking at MTUs as well, but I'm not hopeful as ICMP does not work for me either.

~ ♖ ping twitter.com
PING twitter.com (104.244.42.193) 56(84) bytes of data.
From li807-193.members.linode.com (104.237.131.193) icmpseq=1 Destination Host Unreachable From li807-193.members.linode.com (104.237.131.193) icmpseq=2 Destination Host Unreachable
From li807-193.members.linode.com (104.237.131.193) icmpseq=3 Destination Host Unreachable From li807-193.members.linode.com (104.237.131.193) icmpseq=4 Destination Host Unreachable
From li807-193.members.linode.com (104.237.131.193) icmpseq=5 Destination Host Unreachable From li807-193.members.linode.com (104.237.131.193) icmpseq=6 > Destination Host Unreachable
^C
--- twitter.com ping statistics ---
7 packets transmitted, 0 received, +6 errors, 100% packet loss, time 6090ms
pipe 4

EDIT: I've run the mtr utility but am not sure what to do with its output:

~ ♖ mtr -rw google.com
Start: Sat Apr 28 14:15:36 2018
HOST: linode01                    Loss%   Snt   Last   Avg  Best  Wrst StDev
  1.|-- 2600:3c00::226:51ff:fec4:41  0.0%    10    1.3   1.2   1.0   1.3   0.0
  2.|-- 2600:3c00:2222:14::1         0.0%    10    0.7   0.8   0.7   1.0   0.0
  3.|-- 2600:3c00:2222:10::1         0.0%    10    0.9   0.8   0.6   0.9   0.0
  4.|-- eqix-da1.google.com          0.0%    10    1.4   1.4   1.3   1.4   0.0
  5.|-- 2001:4860:0:e02::1           0.0%    10    2.9   2.5   2.4   2.9   0.0
  6.|-- 2001:4860:0:1::209f          0.0%    10    2.5   2.7   2.1   5.9   1.1
  7.|-- dfw25s25-in-x0e.1e100.net    0.0%    10    1.3   1.4   1.3   1.4   0.0
~ ♖ mtr -rw twitter.com
Start: Sat Apr 28 14:20:44 2018
HOST: linode01 Loss%   Snt   Last   Avg  Best  Wrst StDev
~ ♖ dig twitter.com

; <<>> DiG 9.10.5-P2-RedHat-9.10.5-2.P2.fc24 <<>> twitter.com
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 15222
;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 9, ADDITIONAL: 1

;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;twitter.com.                   IN      A

;; ANSWER SECTION:
twitter.com.            566     IN      A       104.244.42.193
twitter.com.            566     IN      A       104.244.42.129

;; AUTHORITY SECTION:
twitter.com.            2409    IN      NS      a.r06.twtrdns.net.
twitter.com.            2409    IN      NS      d01-01.ns.twtrdns.net.
twitter.com.            2409    IN      NS      d01-02.ns.twtrdns.net.
twitter.com.            2409    IN      NS      ns1.p34.dynect.net.
twitter.com.            2409    IN      NS      ns2.p34.dynect.net.
twitter.com.            2409    IN      NS      ns3.p34.dynect.net.
twitter.com.            2409    IN      NS      ns4.p34.dynect.net.
twitter.com.            2409    IN      NS      r01-01.ns.twtrdns.net.
twitter.com.            2409    IN      NS      r01-02.ns.twtrdns.net.

;; Query time: 0 msec
;; SERVER: 96.126.122.5#53(96.126.122.5)
;; WHEN: Sat Apr 28 14:34:12 UTC 2018
;; MSG SIZE  rcvd: 273

~ ♖ mtr -rw 104.244.42.129
Start: Sat Apr 28 14:34:24 2018
HOST: linode01 Loss%   Snt   Last   Avg  Best  Wrst StDev